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find the upper and lower bounds for definite integral sign, a=1, b=6, sqrt(x) dx. partitions are as follow: x0=1, x1= 3, x2=6 of the interval [1,6] upper sum: 3sqrt(3) + 3sqrt(6) lower sum: 3sqrt(3) + 3 but this is incorrect.

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  1. Sums-Calc

    find the upper and lower bounds for definite integral sign, a=1, b=6, sqrt(x) dx. partitions are as follow: x0=1, x1= 3, x2=6 of the interval [1,6] upper sum: 3sqrt(3) + 3sqrt(6) lower sum: 3sqrt(3) + 3 but this is incorrect. can someone explain what i did
  2. Upper-lower bounds-solved

    find the upper and lower bounds for definite integral sign, a=1, b=6, sqrt(x) dx. partitions are as follow: x0=1, x1= 3, x2=6 of the interval [1,6] upper sum: 3sqrt(3) + 3sqrt(6) lower sum: 3sqrt(3) + 3 but this is incorrect. can someone explain what i did
  3. 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 evaluate
  4. Calculus

    Solve these indefinite and definite integrals. [integration sign] 4j-5j^3 dj I got 2j^2 - 5/4j^4... is this my final answer? If j is the variable, for the indefinite integral you have to add a constant. For the definite integral, you have to put in the
  5. 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
  6. Calculus Fundamental Theorem

    Evaluate the definite integral. function: (t+8)(t^2+3) with respect to variable t lower limit: -sqrt(2) upper limit: sqrt(2)
  7. Calculus

    We're doing a lab in my Calc II class and I'm stuck on this question. I tried to do it by looking at instructions for a similar question in the book, but it made me more confused. Here is the question and my work: Find the area of the region enclosed by
  8. calculus

    Evaluate the definite integral: upper number of the integral is 6 lower number is 2(4x^2+5)/sqrt of x*dx
  9. 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
  10. 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
  11. 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
  12. ap calculus

    Which of the following definite integrals gives the length of y = e^(e^x) between x=0 and x=1? All the answers are preceded by the integral sign from 0 to 1. (a) sqrt[1 + e^(2*(x+e^x))] dx (b) sqrt[1 + e^(4x)] dx (c) sqrt[1 + e^(x+e^x)] dx (d) sqrt[1 +
  13. Calculus Area between curves

    Evaluate the definite integral: sqrt(8-2x) lower limit=-7 upper limit=0 I got -(1/3)(8-2x)^(3/2) and it was wrong. Please Help! Thanks in advance!
  14. Math (Calculus II) (Volume Revolution Setup)

    Consider the graph of y^2 = x(4-x)^2 (see link). Find the volumes of the solids that are generated when the loop of this graph is revolved about (a) the x-axis, (b) the y-axis, and (c) the line x = 4. goo.gl/photos/v5qJLDztqsZpHR9d7 I'm just having trouble
  15. Calculus

    Which of the following integrals correctly computes the volume formed when the region bounded by the curves x^2 + y^2 = 25, x = 4 and y = 0 is rotated around the y-axis? A. pi ∫ upper bound of 3 and lower bound of 0 ( sqrt(25 - y^2) -4)^2 dy B. pi ∫
  16. abstract algebra

    Suppose K = {{2,3,4,5,6,7},{2,5,7,8,12},{1,2,3,5,7,9,13,20}}. Find three upper bounds for K in P(N) and three lower bounds. Does K have a least upper bound? Does K has a greatest lower bound?
  17. abstract algebra

    Suppose K = {{2,3,4,5,6,7},{2,5,7,8,12},{1,2,3,5,7,9,13,20}}. Find three upper bounds for K in P(N) and three lower bounds. Does K have a least upper bound? Does K has a greatest lower bound?
  18. Calculus

    The definite integral of x*(sqrt x^2-400) with an upper limit of 29 and lower limit of 20. After using U-substitution and plugging in the limits I keep getting 32.078 which is wrong, and apparently the right answer is 3087. What am I doing wrong?!?! Please
  19. 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
  20. 12th Calculus

    1. Explain why the function f(x)=(x^2-4)/(x-2) is not continous on [0,3]. what kind of discontinuity occurs? 2. use areas to show that integral sign with the upper limit of 3 and a lower limit of 0 (x^2-4/x-2)dx=10.5 3. use the area to show that intergral
  21. Calculus

    Find d/dx integral(with upper bound of 4x and lower bound of 1) of square root of t^2 +1 dt. A. sqrt(4x+1) B. sqrt(16x^2+1) + sqrt(2) C. 4 sqrt(16x^2+1) D. sqrt(16x^2+1)
  22. Calculus check

    The functions f and g are given by f(x)=sqrt(x^3) and g(x)=16-2x. Let R be the region bounded by the x-axis and the graphs of f and g. A. Find the area of R. B. The region R from x=0 to x=4 is rotated about the line x=4. Write, but do not evaluate, an
  23. math

    1.integral cos(x)sqrt(sin(x))dx. upper limit pi and lower limit 0 2.integral 1/sqrt(x)(sqrt(x) +1)^2. Upper limit is 4 and lower limit is 1.
  24. math

    Sorry I posted this question earlier with a error. Can anyone help me solve this now? Can someone help me answer this? If a < 5 the define integral [a, 4] 2.4e^(1.4x)dx = 44 Find the value a Define integral = integral sign a = lower limit 5 = upper limit
  25. math

    How do you find the definite integral of an absolute function? ∫_0^3|2x-3| lower limit= 0 upper limit = 3
  26. calc

    i need to find the definite integral from 0 to 2|b| of .... x divided by sqrt(x^2 + b^2) dx im having a lot of trouble, thanks in advance Let u = x^2 + b^2 du = 2x dx The integrand becomes (1/2) u^(-1/2) du and the integral of this is u^(1/2) = sqrt(x^2 +
  27. 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
  28. math

    Can someone help me answer this? If a < 5 the define integral [a, 4] 2.4e^(1.4x)dx = 44 Find the value a Define integral = integral sign a = lower limit 4 = upper limit
  29. Calculus

    Function f(x) is positive, increasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the upper sum, lower sum, and trapezoidal rule approximations for the value of
  30. Calculus

    1. Find the are between the curves y=e^x and y=4-x^2 graphically. a.) set up the integral b.) include bounds rounded to three decimal places c.) use integral function on calculator 2. Find the area of the "triangular" region bounded by y=4-x on the left,
  31. math

    Evaluate definite integral of (2x+2)(x^2 + 2x -5)^5dx upper limit 2 and lower limit 1
  32. Calculus Fundamental Theorem

    Evaluate the definite integral. function: x+13 with respect to variable x lower limit:0 upper limit:22
  33. calculus

    Calculate definite integral of dx/(x^4 * sqrt(x^2 + 3)) Over (1,3) I start with the substitution x = sqrt(3)*tan t so: sqrt(x^2 + 3) = sqrt(3) * sec t dx = sqrt(3) * sec^2 t dt x^4 = 9 * tan^4 t The integral simplifies to: = dt/(tan^3 t * sin t) How do I
  34. Calculus

    "Leave the answer as a definite integral, but indicate how it could by evaluated by using the fundamental theorem of calculus." I solved the problem to a definite integral. Proceeding via the fundamental theorem, would involve finding the indefinite
  35. 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]
  36. algebra

    Given that XY =21 and 1 < x < 2, find the sum of the upper and lower bounds of Y. Express your answer as a decimal.
  37. calculus

    Use the Upper Bound theorem to find an integral upper bound and the Lower Bound Theorem to find an integral lower bound of the zeros of the function. 3x^4 - x^3 - 8x^2 - 3x - 20. This is one of the problems from my summer review and I can't find anything
  38. calc check: curve length

    Find the length of the curve y=(1/(x^2)) from ( 1, 1 ) to ( 2, 1/4 ) [set up the problem only, don't integrate/evaluate] this is what i did.. let me know asap if i did it right.. y = (1/(x^2)) dy/dx = (-2/(x^3)) L = integral from a to b for:
  39. calculus

    Assuming that: Definite Integral of e^(-x^2) dx over [0,infinity] = sqrt(pi)/2 Solve for Definite Integral of e^(-ax^2) dx over [-infinity,infinity] I don't know how to approach the new "a" term. I can't use u-substitution, integration by parts, partial
  40. Calc. Help Please.

    Find the value of the definite integral using sums, not antiderivatives: int= integral sign int((x + 2)/(x^(3/2)),x= 16..25)dx Please help... even just showing me how to get started would be greatly appreciated.
  41. Calc,

    Find the value of the definite integral: int= integral sign int((x + 2)/(x^(3/2)),x= 16..25)dx I have no idea how to start this... would I get rid of the fraction?
  42. Maths

    Upper and lower bounds 7.43 to 2 dp
  43. calculus solved

    evaluate integral definite integral sign a=1 b=8 4(x^(2/3)+14)^3/((x^(1/3))) dx I get u= x^2/3 + 14 then du= 2/3 * x^(-1/3) dx 6 { u^4/4 | a=1 b=8 Then I get 3u^4/2 | a=1 b=8 2048-1.5= 2046.5 Is this correct. thank you all.
  44. Calc

    (1/1+(4/n))(4/n)+(1/1+(8/n))(4/n)+(1/1+(12/n))(4/n)+....+(1/1+(4n/n))(4/n) is a right Riemann Sum for a certain definite integral. Integral 1 to b, f(x) dx. using a partition of the interval [1,b] into n subintervals of equal length. Then the upper limit
  45. Calc.

    Find the value of the definite integral using sums, not antiderivatives: int= integral sign int((x + 2)/(x^(3/2)),x= 16..25)dx Please help.
  46. calculus

    using the fundamental theorem of calculus what is the derivative of the definite integral from x^3 to sqrt x of (sqrt t) sin t dt
  47. Calculus

    I'm having trouble with the following problem: Find the volume of the solid generated by revolving the region about the given line. The region is in the first quadrant bounded above by the line y= sqrt 2, below by the curve y=secxtanx, and on the left by
  48. math

    Can someone help me answer this? Determine F ' (x) and F ' (1) if F(x) = integral sign lower limit = 4, upper limit = x 4t^10 (2 t^(1) 0 + 8 ln t) ^4 dt a) F ' (x) = b) F' (1) =
  49. Math - PLEASE HELP

    Can someone help me answer this? Determine F ' (x) and F ' (1) if F(x) = integral sign lower limit = 4, upper limit = x 4t^10 (2 t^(1) 0 + 8 ln t) ^4 dt a) F ' (x) = b) F' (1) =
  50. Math

    Can someone help me answer this? Determine F ' (x) and F ' (1) if F(x) = integral sign lower limit = 4, upper limit = x 4t^10 (2 t^(1) 0 + 8 ln t) ^4 dt a) F ' (x) = b) F' (1) =
  51. math

    Evaluate the integral upper limit sqrt11 and lower limit 1 of (s^2 + sqrt 5)/ s^2
  52. calculus

    Evaluate the integral upper number is 8 lower number is 1 1/x^2 times sqrt of (1 + 1/x) dx
  53. Math

    The following sum [(sqrt(36-((6/n)^2))).(6/n)] + [(sqrt(36-((12/n)^2))).(6/n)]+ ... + [(sqrt(36-((6n/n)^2))).(6/n)] is a right Riemann sum for the definite integral F(x) dx from x=0 to 6 Find F(x) and the limit of these Riemann sums as n tends to infinity.
  54. Calculus

    The following sum [(sqrt(36-((6/n)^2))).(6/n)] + [(sqrt(36-((12/n)^2))).(6/n)]+ ... + [(sqrt(36-((6n/n)^2))).(6/n)] is a right Riemann sum for the definite integral F(x) dx from x=0 to 6 Find F(x) and the limit of these Riemann sums as n tends to infinity.
  55. Maths

    The following sum [(sqrt(36-((6/n)^2))).(6/n)] + [(sqrt(36-((12/n)^2))).(6/n)]+ ... + [(sqrt(36-((6n/n)^2))).(6/n)] is a right Riemann sum for the definite integral F(x) dx from x=0 to 6 Find F(x) and the limit of these Riemann sums as n tends to infinity.
  56. Calculus

    The following sum [(sqrt(36-((6/n)^2))).(6/n)] + [(sqrt(36-((12/n)^2))).(6/n)]+ ... + [(sqrt(36-((6n/n)^2))).(6/n)] is a right Riemann sum for the definite integral F(x) dx from x=0 to 6 Find F(x) and the limit of these Riemann sums as n tends to infinity.
  57. calculus please help!!

    Find the range of the function F(x)= definite integral from [-6,x] of sqrt(36-t^2)dt. [0, 36π] [0, 18π]*** [-6, 6] [-6, 0]
  58. Calculus URGENT test tonight

    Integral of: __1__ (sqrt(x)+1)^2 dx The answer is: 2ln abs(1+sqrt(x)) + 2(1+sqrt(X))^-1 +c I have no clue why that is! Please help. I used substitution and made u= sqrt(x)+1 but i don't know what happened along the way! Your first step was a good one.
  59. calculus

    Starting with F(x) = integral (-2, x) 3t^2(cos (t^3) + 2) dt, use substitution u(t)=t^3 to rewrite the definite integral. You should get a new equivalent expression for F(x), which consists of this new definite integral.
  60. Calculus

    Can someone explain to me how to do these? Given the following definite integral and n=4 answer the following questions. (Round your answers to six decimal places.) 1. Use the Trapezoidal Rule to approximate the definite integral. Answer: T4= 2. Use the
  61. Calculus

    Find the definite integral that represents the arc length of the curve y=sqrt(x) over the interval [0, 3]
  62. Calculus

    Evaluate the integral by interpreting it in terms of areas. bounds from -1 to 0. 3+sqrt(1−x2) dx
  63. Math

    Evaluate the following definite integral. sqrt(11 x)(sqrt(x) + sqrt(11)) dx between(0,1)
  64. Calculus

    Would someone clarify this for me... Is antiderivatives just another name for intergral and why is intergral of a function is the area under the curve? Antiderivatives is another word for integral. Why area? THink on this...the integral is the sum of all
  65. Integral

    Find dy/dx and d2y/dx2 if y= definite integral sign where a= 1 and b= 3x 1/(t^2+t+1) dt how do i even start. do i integrate and then plug in a and b? plz help.
  66. integral

    Find dy/dx and d2y/dx2 if y= definite integral sign where a= 1 and b= 3x 1/(t^2+t+1) dt how do i even start. do i integrate and then plug in a and b? plz help.
  67. CALC

    I just need help with changing the order of integration. I can do the actually integral by myself. Thank you :) int f(x,y) dydx where y bounds= 1 to e^x and x bounds= 0 to 4 I thought the new bounds were int f(x,y) dxdy x= 0 to log(y) y= 1 to e^4 Please
  68. calculus

    The following definite integral can be evaluated by subtracting F(B) - F(A), where F(B) and F(A) are found from substituting the limits of integration. \int_{0}^{4} \frac{1600 x +1200 }{(2 x^2 +3 x +1)^5}dx After substitution, the upper limit of
  69. Maths

    How do we caclualate 10 * 9 \ 1 One time in the lower bounds giving it the the nearest whole no. Another in the upper " """"""" "" """""""""""""""""""""
  70. Math

    Estimate the are under the curve f(x)=x^2-4x+5 on [1,3]. Darw the graph and the midpoint rectangles using 8 partitions. Show how to calculate the estimated area by finding the sum of areas of the rectangles. Find the actual area under the curve on [1,3]
  71. 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 surface
  72. Math

    Let A denote the portion of the curve y = sqrt(x) that is between the lines x = 1 and x = 4. 1) Set up, don't evaluate, 2 integrals, one in the variable x and one in the variable y, for the length of A. My Work: for x: integral[4,1] sqrt(1+(dy/dx)^2) dy/dx
  73. ap statistics

    In a survey, 600 mothers and fathers were asked about the importance of sports for boys and girls. Of the parents interviewed, 70% said the genders are equal and should have equal opportunities to participate in sports. B. Using the normal approximation
  74. Calculus

    so we are doing integrals and I have this question on my assignment and I can't seem to get it, because we have the trig substituion rules, but the number isn't even so its not a perfect square and I just cant get it, so any help would be greatly
  75. 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
  76. 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
  77. calculus-extrema

    Find and classify the relative maxima and minima of this function f(x)= definite integral sign where a=0 and b=x. t^2-4/(1+(cos^2(t)) dt what should my value for u be? is it just t. not sure how to even tackle this problem.
  78. Extrema-Calc

    Find and classify the relative maxima and minima of this function f(x)= definite integral sign where a=0 and b=x. t^2-4/(1+(cos^2(t)) dt what should my value for u be? is it just t. not sure how to even tackle this problem.
  79. Calc. Checking Answer

    Find the antiderivative by hand in each case. S stands for the integral sign I want to make sure I am doing these correctly. A) S x*sqrt(10 + x^2) dx So, u= 10 + x^2 du= 2xdx du/2= xdx (1/2) S sqrt(u) du (1/2)*((u^(3/2))/(3/2)) (1/2)*(2/3)*(u^(3/2))
  80. Calculus (Checking Answer)

    Find the antiderivative by hand in each case. S stands for the integral sign A) S x*sqrt(10 + x^2) dx So, u= 10 + x^2 du= 2xdx du/2= xdx (1/2) S sqrt(u) du (1/2)*((u^(3/2))/(3/2)) (1/2)*(2/3)*(u^(3/2)) (1/3)*(u^(3/2)) = (1/3)*(10 + x^2)^(3/2)
  81. Calculus

    Find the exact area of the region enclosed by the square root of (x) + the square root of (y) is = 1; x = 0 and y = 0. I moved the first equation around to get: y = [1- the square root of (x) ] ^2 Unfortunately, this gives me bounds from 1 to 1. So I'm
  82. calculus help me pllllllllllz

    Find out what kind of improper integral is given below §dx/{x^4+4}....?,hence evaluate the integral with upper boundary=infinity lower boundary =0 i need help plz show me full work
  83. mathematics

    Use a definite integral to find the area of the upper right quarter of the circle of radius 1 with the centre at the origin of the coordinate plane. (the integration of √1 − x^2dx =1/2(x√1 − x^2 + arcsin x)).
  84. Calculus

    Graph the curve and find its exact length. x = e^t + e^-t, y = 5 - 2t, from 0 to 3 Length = Integral from 0 to 3 of: Sqrt[(dx/dt)^2 + (dy/dt)^2] dx/dt = e^t - e^-t, correct? dy/dt = -t^2 - 5t, correct? So: Integral from 0 to 3 of Sqrt[(e^t - e^-t)^2 +
  85. Math: Need Answer to study for a quizz. Help ASAP

    Estimate the area under the curve f(x)=x^2-4x+5 on [1,3]. Darw the graph and the midpoint rectangles using 8 partitions. Show how to calculate the estimated area by finding the sum of areas of the rectangles. Find the actual area under the curve on [1,3]
  86. math

    calculate the upper limit for the definite integral from -2 to 2. oh x^2+1 dx with the partition P=-2,-1,0,1,2
  87. math

    Note: You can get full credit for this problem by just answering the last question correctly. The initial questions are meant as hints towards the final answer and also allow you the opportunity to get partial credit. Consider the definite integral from
  88. Math emergency I have 10 minutes to submit it.

    Evaluate the definite integral. x sqrt(13 x^2 + 36)dx between (0,1)
  89. Calc 2

    Evaluate the definite integral from 0 to 1 of (x^2)sqrt(5x+6)dx
  90. Calculus Please Help

    Evaluate the indefinite integral Note: Use an upper-case "C" for the constant of integration. integral sqrt(100x^2-400)/x dx Ty
  91. calc: arc length

    find the exact length of this curve: y = ( x^3/6 ) + ( 1/2x ) 1/2
  92. Math

    How do you solve the definite integral of sqrt( (t+1)^2 ) from 0 to 1. I tried using u-substitution, but I am not sure if this is the way to go?
  93. Calc - Evaluating Integrals

    1.) upper bound: pi lower bound: 0 8sinx / sqrt(5-4cosx) dx 2.) upper bound: sqrt 3 lower bound: 0 4x / sqrt(x^2 + 1) dx 3.) upper bound: 1 lower bound: -1 (dx) / (3x-4)
  94. math calculus

    Let f be twice differentiable with f(0)=12, f(3)=9, and f '(3)=4.Evaluate the integral upper limit 3 and lower integral 0 xf'' (x)dx
  95. Calculus

    Find the exact coordinates of the centroid. y = sqrt[x], y = 0, x = 9. -------------- Is this basically 1/4 of an oval/ellipse? If so then the area would be: pi*9*3, correct? So the X coordinate would equal: 1/Area * Integral from 0 to 9 of (x*f(x))*dx
  96. calc: avg value

    Find the average value of the function "f(x) = x^2 sqrt(1+x^3)" on the interval [0,2]. and this is what i did.. please check for mistakes. thanks :D f(x) = x^2 sqrt(1+x^3), [0,2] f ave = (1/(b-a))*inegral of a to b for: f(x) dx f ave = (1/(2-0))*integral
  97. math,algebra,help

    Directions are simplify by combining like terms. x radiacal 18 -3 radical 8x^2 can someone show me how to do these types of problems. thanks I cant determine the second term. For the first, I think you meant x sqrt(18) which reduces to x sqrt (9*3) or 3x
  98. math

    integrals evaluate the definite integral from 1 to 9 of ((x-1) / (sqrt x)) dx ? Would this one be a u sub? evaluate the integral from 0 to 10 of abs value (x-5) dx? I think this one would be split but not sure how or why?
  99. calc check: average value

    Find the average value of the function "f(x) = x^2 sqrt(1+x^3)" on the interval [0,2]. and this is what i did.. please check for mistakes. thanks :D f(x) = x^2 sqrt(1+x^3), [0,2] f ave = (1/(b-a))*inegral of a to b for: f(x) dx f ave = (1/(2-0))*integral
  100. Calculus

    Hi. In an integration solution, the integral of (1/(sqrt (8-u squared)) is written as arcsin(u/sqrt 8), but I don't see how they got it. When I did it I got (1/8)*(arcsin(u*sqrt8)). What I did was take sqrt8 common in the denominator to get it in the form

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