1. Calculus

    Calculate the following integral and determine whether it's convergent, or divergent. integral at [-3,0] x dx / sqr(9 - x^2)
  2. Calculus

    Evaluate the integral: 16csc(x) dx from pi/2 to pi (and determine if it is convergent or divergent). I know how to find the indefinite integral of csc(x) dx, but I do not know how to evaluate the improper integral.
  3. Calculus

    Use the Comparison Theorem to determine whether the following integral is convergent or divergent. S= integral sign b=infinity and a=1 S(9(cosx^2))/ (1+x^2) dx
  4. calculus

    is this correct? use the integral test to determine if this series is convergent or divergent: the series from n=2 to infinity of 1/(n*square root of (ln(n))) I said it was divergent because the integral went to infinity
  5. calculus

    Determine whether the integral is convergent or divergent.If it is convergent, evaluate it. form -infinity to 0 x/(x^4+25)dx
  6. calculus

    Determine whether the integral is convergent or divergent.If it is convergent, evaluate it. from 0 to infinity e^(-y^1/2)dy
  7. calculus (integral test)

    use integral test to determine whether the series is convergent or divergent infinity (sum symbol) n=1 1/(sqrt n)^5
  8. Calculus

    Evaluate the integral: 16csc(x) dx from pi/2 to pi (and determine if it is convergent or divergent). I know how to find the indefinite integral of csc(x) dx, but I do not know how to evaluate the improper integral, at the following particular step. I know
  9. Calculus

    Determine if convergent or divergent: Integral 1 to infinity of e to the power of (-1/2).
  10. calculus

    Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. from -infinity to infinity 17xe^(-x^2)dx
  11. calculus

    use the integral test to determine whether the series is convergent or divergent ∑ n=9 1/n(ln n)^3
  12. Calculus

    Determine whether the integral is divergent or convergent. If it is convergent, evaluate it and enter that value as your answer. If it diverges to infinity, state your answer as "INF" (without the quotation marks). If it diverges to negative infinity,
  13. Calculus II

    I need to find if the summation of (n^4)/(n^10 + 1) is convergent or divergent from n=1 to infinity. I tried splitting it up into two sums, one being 1/n^6, which would be convergent because p=6>1, and then the other being n^4, but I'm not sure how to
  14. Calculus

    Determine whether the integral is divergent or convergent. If it is convergent, evaluate it and enter that value as your answer. If it diverges to infinity, state your answer as "INF" (without the quotation marks). If it diverges to negative infinity,
  15. calculus

    show that an integral of the form ∫00,a e^(-px) dx is convergent if p>0 and divergent if p<0
  16. calc

    how do you start this problem: integral of xe^(-2x) There are two ways: 1) Integration by parts. 2) Differentiation w.r.t. a suitably chosen parameter. Lets do 1) first. This is the "standard method", but it is often more tedious than 2) You first write
  17. calculus

    Determine whether the following is convergent of divergent. integral(lower limit=0, upper limit=infinity)of sin(x)sin(x^2)dx Thanks
  18. Calculus

    Determine whether the series is convergent or divergent. If it is convergent, find its sum. If it is divergent, enter NONE. sum from 1 to infinity of 1/e^2n. It is convergent, but I do not know how to solve for the sum.
  19. calc asap!

    can you help me get started on this integral by parts? 4 S sqrt(t) ln(t) dt 1 please help! thanks! Integral t^(1/2)Ln(t)dt = 2/3 t^(3/2)Ln(t)- 2/3 Integral t^(1/2) dt = 2/3 t^(3/2)Ln(t) - 4/9 t^(3/2) Simpler method: Integral t^(a)dt = t^(a+1)/(a+1)
  20. Calculus

    If f(x) and g(x) are continuous on [a, b], which one of the following statements is true? ~the integral from a to b of the difference of f of x and g of x, dx equals the integral from a to b of f of x, dx minus the integral from a to b of g of x dx ~the
  21. calculus

    how do you solve the integral of 1/[(square root of x)(lnx)] from 2 to infinity? i did the p- integral theorem with 1/square root of x and got it to be a divergent integral. however i was told this was the wrong way and that i should do it by integration
  22. Calculus

    Hello, I have some calculus homework that I can't seem to get started..at least not on the right track? I have 3 questions 1. integral of [(p^5)*(lnp)dp] I'm using the uv-integral v du formula So first, I'm finding u and I think it's lnp.......so du is 1/p
  23. Convergent/Divergent

    determine whether the series 1 + 1/2^5 + 1/3^5 + 1/4^5 +...is convergent or divergent? How do I tell the difference?
  24. Calculus

    Find the volume of the solid whose base is the region in the xy-plane bounded by the given curves and whose cross-sections perpendicular to the x-axis are (a) squares, (b) semicircles, and (c) equilateral triangles. for y=x^2, x=0, and y=0 (a) integral
  25. Calculus

    Show that the following integral is convergent, Integral, it goes from 0 to infinity dx/(sqrt(x) + x^2)
  26. Calculus

    integral -oo, oo [(2x)/(x^2+1)^2] dx (a) state why the integral is improper or involves improper integral *infinite limit of integration (b) determine whether the integral converges or diverges converges? (c) evaluate the integral if it converges I know
  27. Calculus II/III

    A. Find the integral of the following function. Integral of (x√(x+1)) dx. B. Set up and evaluate the integral of (2√x) for the area of the surface generated by revolving the curve about the x-axis from 4 to 9. For part B of our question , the
  28. calculus

    8). Part 1 of 2: In the solid the base is a circle x^2+y^2=16 and the cross-section perpendicular to the y-axis is a square. Set up a definite integral expressing the volume of the solid. Answer choices: integral from -4 to 4 of 4(16-y^2)dy, integral from
  29. Calculus 2 (Series - Convergent or Divergent?)

    Can someone show me a step by step process and explanation how to solve this problem? 1) Consider the following series. (∞ on top of summation symbol) (k = 1 under the summation symbol) ∑ k(k+15)/(k+13)^2 Determine whether the series is
  30. Calculus

    Determine whether the series is convergent or divergent. If it is convergent, find its sum. If it is divergent, enter NONE. sum from 1 to infinity of (5^n+4^n)/20^n It is convergent, but I do not know how to find the sum.
  31. Calculus

    Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If it diverges to infinity, state your answer as INF. If it diverges to negative infinity, state your answer as MINF. If it diverges without being infinity or
  32. calculus

    Determine whether the series is convergent o divergent and say what test you used to solve it. (d) sum n=1 to infinity (5n)^(3n) / (5^n + 3)^n (e) sum k=1 to infinity 5 / sqr(2k - 1)
  33. Integral Calculus - Series

    Find if series is convergent or divergent. Series from n=2 to infinity (4n+7)/(3n^3 -8n)
  34. calculus

    1. integral -oo, oo [(2x)/(x^2+1)^2] dx 2. integral 0, pi/2 cot(theta) d(theta) (a) state why the integral is improper or involves improper integral (b) determine whether the integral converges or diverges converges? (c) evaluate the integral if it
  35. Calculus

    For what values of p>0 does the series Riemann Sum [n=1 to infinity] 1/ [n(ln n) (ln(ln n))^p] converge and for what values does it diverge? You need to let the summation start at n = 3 to avoid the singularity at n = 1 (although you can formally take
  36. integration by parts

    s- integral s ln (2x+1)dx ? = ln(2x+1)x - s x d( ln (2x+1)) = ln(2x+1)x- s x [(2x+1)'/ (2x+1)] dx = ln(2x+1)x- s x [(2)/ (2x+1)] ?... then i'm confused... "ln(2x+1)x- s x [(2)/ (2x+1)] ?... then i'm confused..." x [(2)/ (2x+1)] = 2x/(2x+1) =
  37. Calculus

    Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. A (sub n)=((4n-7)/(4n+9))
  38. Quick calc question

    If f(x) and g(x) are continuous on [a, b], which one of the following statements is false? the integral from a to b of the sum of f of x and g of x, dx equals the integral from a to b of f of x, dx plus the integral from a to b of g of x dx the integral
  39. Calc 121

    How do you integrate using substitution: the integral from 1 to 3 of: ((3x^2)+(2))/((x^3)+(2x)) There is a trick to this one that grealy simplifies the integral. Let u = x^3 + 2x. Then du = (3x^2 + 2)dx The integral then bemoces just the integral of du/u,
  40. Definite integral by parts (correction)

    Hello, I just wanted to verify if my work was good. Calculate the following integral by parts: ∫ upper limit is 1/5 and lower limit is 1/10. of 10sin^-1 (5x)dx so first I named the variables: u = 10 sin^-1 (5x) du = 50 / sqr(1-25x^2) dv = dx v = x so
  41. Math/Calculus

    How would I solve the following integral with the substitution rule? Integral of: [(x^3)*(1-x^4)^5]dx Put 1-x^4 = y Then -4x^3 dx = dy Integral is then becomes: Integral of -1/4 y^5 dy ok, thanks a lot! I got it now.
  42. calculus

    is the sum from k=1 to infinity of 1/(k^2+1) convergent? i said it was because the integral is convergent
  43. calc

    find integral using table of integrals ) integral sin^4xdx this the formula i used integral sin^n xdx =-1/n sin^n-1xcosx +n-1/n integral sin^n-2 using the formula this is what i got: integral sin^4xdx=-1/4sin^3xcosx+3/4 integral sin^2xdx= -1/2sinxcosx+1/2
  44. calculus

    There are four integrals: 1) definite integral x/(1+x^4)dx b/w 0_infinity 2) definite integral (x^2)/(1+x^4)dx b/w 0_infinity 3) definite integral (x^3)/(1+x^4)dx b/w 0_infinity 4) definite integral (x^4)/(1+x^4)dx b/w 0_infinity Which of these integrals
  45. calculus

    There are four integrals: 1) definite integral x/(1+x^4)dx b/w 0_infinity 2) definite integral (x^2)/(1+x^4)dx b/w 0_infinity 3) definite integral (x^3)/(1+x^4)dx b/w 0_infinity 4) definite integral (x^4)/(1+x^4)dx b/w 0_infinity Which of these integrals
  46. math

    LEt f and g be continous functions with the following properties i. g(x) = A-f(x) where A is a constant ii. for the integral of 1 to 2 f(x)dx= the integral of 2 to 3 of g(x)dx iii. for the integral from 2 to 3 f(x)dx = -3A a find the integral from 1 to 3
  47. calculus

    LEt f and g be continous functions with the following properties i. g(x) = A-f(x) where A is a constant ii. for the integral of 1 to 2 f(x)dx= the integral of 2 to 3 of g(x)dx iii. for the integral from 2 to 3 f(x)dx = -3A a find the integral from 1 to 3
  48. calculus

    LEt f and g be continous functions with the following properties i. g(x) = A-f(x) where A is a constant ii. for the integral of 1 to 2 f(x)dx= the integral of 2 to 3 of g(x)dx iii. for the integral from 2 to 3 f(x)dx = -3A a find the integral from 1 to 3
  49. Math

    Calculate the integrals if they converge. 10.) Integral from 1 to infinity of X/4+X^2 dx 14.) integral from Pi/2 to Pi/4 of Sin X / sqrt cos x dx 22.) integral from 0 to 1 of ln x/x dx I'm having problems with working these out to figure out if they
  50. Math/Calculus

    How would I evaluate the following integral by using integration by parts? Integral of: (t^3)(e^x)? You mean (x^3)(e^x)? x^3 exp(x) dx = x^3 d[exp(x)] = d[x^3 exp(x)] - exp(x) d[x^3] = d[x^3 exp(x)] - 3 x^2 exp(x) dx So, if you integrate this you get x^3
  51. Pre-calculus

    Which of the following series is divergent? a) 1+3(1/4)+9(1/4)^2+27(1/4)^3... b) 1+3(1/5)+9(1/5)^2+27(1/5)^3... c) 1+3(1/7)+9(1/7)^2+27(1/7)^3... d) 1+3(1/2)+9(1/2)^2+27(1/2)^3... How do you determine if a series in convergent or divergent??? The book that
  52. calculus (please with steps and explanations)

    consider the function f that is continuous on the interval [-5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each integral: (a) definite
  53. calculus

    consider the function f(x) = e^x(sinNx) on the interval [0,1] where N is a positive integer. a) Compute the integral from 0 to 1 of f(x). Evaluate this integral when N=5, N=10, and N=100. B) What happens to the graph and to the value of the integral as
  54. calculus

    consider the function f(x) = e^x(sinNx) on the interval [0,1] where N is a positive integer. a) Compute the integral from 0 to 1 of f(x). Evaluate this integral when N=5, N=10, and N=100. B) What happens to the graph and to the value of the integral as
  55. Calculus

    Use the symmetry of the graphs of the sine and cosine functions as an aid in evaluating each definite integral. (a) Integral of sinx*dx from -pi/4 to pi/4 (b) Integral of cosx*dx from -pi/4 to pi/4 (c) Integral of cosx*dx from -pi/2 to pi/2 (d) Integral of
  56. Calculus

    Can someone look over my work and tell me if my steps look correct? I'm trying to correct some problems that looked wrong. Instructions: Find the total areas between the given curves. 1. x= (y^3) and x=(y^2) on the interval [0,1] (integral from 0 to 1 of)
  57. Math

    Find the integrals. (show steps) (integral sign) xe^(4x^2) I think this how is how its done: (integral sign) xe^(4x^2) it's a u du problem let u=4x^2 so, du=8x dx now you have an x already so all u need is 8 inside and and 1/8 outside the integral [1/8]
  58. Physics, Calculus(alot of stuff together)= HELP!!

    A rod extending between x=0 and x= 14.0cm has a uniform cross- sectional area A= 9.00cm^2. It is made from a continuously changing alloy of metals so that along it's length it's density changes steadily from 2.70g/cm^3 to 19.3g/cm^3. a) Identify the
  59. Quick calc question

    Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = 1 – x2 and the x-axis? the integral from 0 to 1 of the quantity 1 minus x squared, dx plus the integral from 1 to 2 of the quantity 1 minus x
  60. Quick calc question

    Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = 1 – x2 and the x-axis? the integral from 0 to 1 of the quantity 1 minus x squared, dx plus the integral from 1 to 2 of the quantity 1 minus x
  61. Quick calc question

    Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = 1 – x2 and the x-axis? the integral from 0 to 1 of the quantity 1 minus x squared, dx plus the integral from 1 to 2 of the quantity 1 minus x
  62. Integral

    That's the same as the integral of sin^2 x dx. Use integration by parts. Let sin x = u and sin x dx = dv v = -cos x du = cos x dx The integral is u v - integral of v du = -sinx cosx + integral of cos^2 dx which can be rewritten integral of sin^2 x = -sinx
  63. Calculus II

    Integrate using integration by parts (integral) (5-x) e^3x u = 5-x du = -dx dv = e^3x v = 3e^3x I wonder if this is right so far. = uv - (integral) v du = (5-x)(3e^3x) - (integral) (-3e^3x) =(5-x)(3e^3x) + (integral) (3e^3x) = (5-x)(3e^3x) + 9e^3x + C
  64. Calc

    Evaluate the integral using any method: (Integral)sec^3x/tanx dx I started it out and got secx(1tan^2x)/tanx. I know I just have to continue simplifying and finding the integral, but I'm stuck on the next couple of steps. Also, I have another question
  65. Calculus (urgent help)

    consider the function f that is continuous on the interval [-5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each integral: (a) definite
  66. double integral

    1. Sketch the region of integration & reverse the order of integration. Double integral y dydz... 1st (top=1, bottom =0)... 2nd(inner) integral (top=cos(piex), bottom=(x-2)... 2. Evaluate the integral by reversing the order of integration. double integral
  67. Calc

    Hello im trying to integrate tan^3 dx i have solved out the whole thing but it doesnt match up with the solution.. this is what i did: first i broke it up into: integral tan^2x (tanx) dx integral (sec^2x-1)(tanx) dx then i did a u substitution u = secx du
  68. Calc

    Hello im trying to integrate tan^3 dx i have solved out the whole thing but it doesnt match up with the solution.. this is what i did: first i broke it up into: integral tan^2x (tanx) dx integral (sec^2x-1)(tanx) dx then i did a u substitution u = secx du
  69. Calc BC

    1. Find the indefinite integral. Indefinite integral tan^3(pix/7)sec^2(pix/7)dx 2. Find the indefinite integral by making the substitution x=3tan(theta). Indefinite integral x*sqrt(9+x^2)dx 3. Find the indefinite integral. Indefinite integral
  70. Calculus

    Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = 1 – x2 and the x-axis? the integral from 0 to 1 of the quantity 1 minus x squared, dx plus the integral from 1 to 2 of the quantity 1 minus x
  71. Integral Help

    I need to find the integral of (sin x)/ cos^3 x I let u= cos x, then got -du= sin x (Is this right correct?) I then rewrote the integral as the integral of -du/ u^3 and then rewrote that as the integral of - du(u^-3). For this part, I wasn't sure how to
  72. calculus

    how do you determine the convergence of : definite integral from 1--> infinity of lnx/(x^3)? i set the problem as lim (R--->infinity) of the integral of lnx/(x^3) from 1--->R, but i can't compute the integral.
  73. calc 2

    Determine whether the integral converges or diverges. Find the value of the integral if it converges. The integral where b=2 and a=0 (x/x^2-1 dx).
  74. Calculus

    Hello, I'd appreciate any help with the following question below: Information: g(x)= 4 (x+1)^(-2/3) f(x)= ∫ g(t) dt The Question: What is f(26) ? (NOTE: I don't know how to do this on a key board, so I'll just say that while I did type an Indefinite
  75. integral confusion

    integral of Sec[2x]Tan[2x] i know u is sec 2x du=2sec2xtan2x dx what would i have to multiply with du so it would equal tan 2x dx? if my question is confusing, then here's another example of what i'm talking about: integral of (3x-2)^30 dx u=3x-2 du=3 dx
  76. Math (Definite Integrals)

    Sketch the region given by the definite integral. Use geometric shapes and formulas to evaluate the integral (a > 0, r > 0). r ∫ sqrt(r^2 - x^2) dx -r While I recognize that this looks similar to a circle function, I'm not sure how to graph and
  77. Calculus

    Can someone check my work and answer? Evaluate the integral from -1 to 0 of (4x^6+2x)^3(12x^5+1)dx My work: let u=4x^6+2x dx=du/24x^5+2 now we have the integral from -1 to 0 of u^3(12x^5+1)(du/24x^5+2) Simplifies to the integral from -1 to 0 of
  78. calculus

    consider the function f that is continuous on the interval [-5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each integral: (a) definite
  79. calculus

    calculate the indefinite integral 2sec^2x dx (cosx)/(sin^3x) dx calculate the definite integral interval pi/4, pi/12 csc2xcot2x dx
  80. intergrals

    find value of def integral with a=-2 and b=2sqrt(3) definite integral is : x^3 * sqrt(x^2+4) dx for integral i get 1/15 *((4+x^2)^(3/2)) (-8+3x^2) for value i get [1536- 64sqrt(2)]/15 but its' wrong. help please
  81. Calculus

    Find the area of the region bounded by y = x^2, y = 0, x = -1, and x = 2. I tried the integral from -1 to 2 of x^2 and got 3 as the answer. I tried (integral from 0 to 1 of √y + 1) + (integral from 0 to 4 of 2 - √y) and got 13/3. What is wrong with the
  82. math

    Evaluate the following indefinite integral by using the given substitution to reduce the integral to standard form integral cos(9x) dx, u=9x
  83. Calculus 2

    The question is: Evaluate the improper integral for a>0. The integral is: the integral from 0 to infinity, of e^(-y/a)dy Can anyone help me solve this? When I try I get 'a', which apparently is incorrect. Thank you!
  84. Calculus - Integrals

    I have 3 questions, and I cannot find method that actually solves them. 1) Integral [(4s+4)/([s^2+1]*([S-1]^3))] 2) Integral [ 2*sqrt[(1+cosx)/2]] 3) Integral [ 20*(sec(x))^4 Thanks in advance.
  85. Calculus integral

    evaluate the integral: integral from -pi/4 to 0 for the function 6sec^3x dx. it has to be an exact answer and i did it and keep getting it wrong. I got 4sqrt(2)-4ln(-sqrt(2)+1)
  86. Calculus - Integrals

    I have 3 questions, and I cannot find method that actually solves them. 1) Integral [(4s+4)/([s^2+1]*([S-1]^3))] 2) Integral [ 2*sqrt[(1+cosx)/2]] 3) Integral [ 20*(sec(x))^4 Thanks in advance.
  87. Calculus

    F(x) = cos(x) • the integral from 2 to x² + 1 of e^(u² +5)du Find F'(x). When i did this, i got: -2xsin(x)e^((x²+1)² + 5) But my teacher got: -sin(x) • the integral from x² + 1 of e^(u² +5)du + 2xcos(x)e^((x²+1)² + 5) Do you know why the
  88. Calc 2

    a. Integral (x^2)/(sqrt(1+(x^2))) Would I separate these two into 2 separate integrals? Like: Integral of x^2 and the other integral of 1/sqrt(1+(x^2)) b. Integral (x^7)/(ln(x^4))dx Do I use integration by parts for this? I put u= lnx du = 1/x dv = x^7 v =
  89. math

    Evaluate the following indefinite integral by using the given substitution to reduce the integral to standard form integral 2(2x+6)^5 dx, u=2x+6
  90. Math(Please check)

    evaluate the integral integral of 3 to 2 x/(x^2-2)^2 dx u=x^2-2 du=2x dx 1/2 du = x dx integral of 1/u^2 du -1/(x^2-2) Then I plug in 3 and 2 and subtract them form each other -1/(3^2-2) - (-1/(2^2-2) Is this correct?
  91. math

    Evaluate the given integral, where C is the circle with positive orientation. Cauchy integral theorem, integral over C (2z-3)/(z^(2)-4)(z+2) dz, C:|z+3|=3
  92. calculus

    evaluate integral or state that it is diverges integral -oo, -2 [2/(x^2-1)] dx ----------------------------------- integral -oo, -2 [2/(x^2-1)] dx Through partial fractions, I came up with lim [ln(x-1)-ln(x+1)] b, -2 b->-oo I get (ln(3)-0)-(oo-oo)). The
  93. Calculus

    evaluate the integral or state that it diverges. Check if I did it correctly. integral 0,1 dr/r^.999 lim b->0+ integral b, 1 1000r^.001 =-1000
  94. math

    How do I derive the secant reduction rule? Integral (sec x)^n dx = Integral (sec x)^(n-2) * (sec x)^2 dx = Integral ((tan x)^2 + 1)^(n/2-1) * (sec x)^2 dx Doing a substitution with: u = tax x du = (sec x)^2 dx = Integral (u^2 + 1)^(n/2-1) * du At this
  95. Calculus Help Please Urgent!!!

    Prove that the integral on the interval [a,b] of x is equal (b^2-a^2)/2 integral a to be (x)dx = (b^2-a^2)/2 using the definition of a Definite Integral. This is the limit of a sum approach. show steps please!!! Thank you!!!
  96. math

    evaluate the double integral and reverse order of integration [(first integral 0 to 1)(second integral 9y to 9)e^(x^2)dx)dy
  97. math, calculus

    if f(1)=12 and f' is continuous, what is the value of f(4)? integral from 1 to 4 of f'(x)dx = 17 IF the integral of f'(x) dx from 1 to 4 is 17, as you say, then the function f(x), which is the integral with an arbitrary constant, changes by 17 from 1 to 4.
  98. Math

    Determine the integral by making an appropriate substitution integral of 8x cuberoot srqt(4x^2-9) dx let u= 4x^2-9 du= 8x dx I do not know what to do now
  99. Math(Please help)

    Determine the integral by making an appropriate substitution integral of 8x cuberoot srqt(4x^2-9) dx let u= 4x^2-9 du= 8x dx I do not know what to do now
  100. calc check

    <<y=(1/A)*integral from a to b of: (1/2)[f(x)]^2 dx >> If that is the y value of the center of mass, I don't know why the factor (1/2) is there I also don't agree with your calculation of the x value, which should be 1/(ln 2). I agree with you