suppose x S f(t) dt= x^2  2x + 1. Find f(x). 1 S = integral and 1 = lower level, x = upper i don't understand what i'm supposed to find/what to do
107,009 results
calculus integrals
Evaluate the integral by making the given substitution. (Use C for the constant of integration. Remember to use absolute values where appropriate.) integral x^5/x^65 dx, u = x6 − 5 I got the answer 1/6ln(x^65)+C but it was wrong. ps. I wrote the word

calc
Suppose the integral from 2 to 10 of g of x, dx equals 10 and the integral from 8 to 10 of g of x, dx equals negative 6, find the value of the integral from 2 to 8 of onehalf times g of x, dx .

calc
d/dx integral from o to x of function cos(2*pi*x) du is first i do the integral and i find the derivative right. by the fundamental theorem of calculus, if there is an integral from o to x, don't i just plug the x in the function. the integral of the

Calculus
Suppose the integral from 2 to 8 of g of x, dx equals 5, and the integral from 6 to 8 of g of x, dx equals negative 3, find the value of the integral from 2 to 6 of 2 times g of x, dx . 8 MY ANSWER 12 16 4

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

math
suppose x S f(t) dt= x^2  2x + 1. Find f(x). 1 S = integral and 1 = lower level, x = upper i don't understand what i'm supposed to find/what to do and i didn't make any typos.

Calculus check
The functions f and g are given by f(x)=sqrt(x^3) and g(x)=162x. Let R be the region bounded by the xaxis 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

Calculus
Suppose f(x) is a continuous function. Then a function F(x) such that F'(x) = f(x) is called: A.) the indefinite integral of f B.) the antiderivative of f C.) an antiderivative of f D.) a definite integral of f E.) All of the above

calculus
1.Evaluate the integral. (Use C for the constant of integration.) integral ln(sqrtx)dx 2. Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the curves about the given axis. y = 4ex, y = 4e−x, x = 1;

Calculus (Antiderivatives)
Suppose f(x) is a continuous function. Then a function F(x) such that F'(x) = f(x) is called: A.) the indefinite integral of f B.) the antiderivative of f C.) an antiderivative of f D.) a definite integral of f E.) All of the above

Calculus
A population of rabbits starts off at time = 0 with 225 rabbits and increases at a rate of r(t) rabbits per month, where t is in months. A. What does the expression (24 integral 36)r(t)dt represent? B. What does the expression 225 + (0 integral 18) r(t)dt

Math
In the exercise we want to use a substitution to integrate integral xsqrt(x+1)dx. Find the substitution u to transform the integral into integral(u1)u^(1/2)du. u=?

Calculus
Suppose the integral from 2 to 6 of g of x, dx equals 12 and the integral from 5 to 6 of g of x, dx equals negative 3 , find the value of the integral from 2 to 5 of 3 times g of x, dx. A. 45

calculus
1. Find the area of the region bounded by f(x)=x^2 +6x+9 and g(x)=5(x+3). Show the integral used, the limits of integration and how to evaluate the integral. 2. Find the area of the region bounded by x=y^2+6, x=0 , y=6, and y=7. Show all work required in

Calculus
Which of the following integrals can be integrated using partial fractions using linear factors with real coefficients? a) integral 1/(x^41) dx b) integral (3x+1)/(x^2+6x+8) dx c) integral x^2/(x^2+4) d) None of these

calculus
suppose x S f(t) dt= x^2  2x + 1. Find f(x). 1 S = integral and 1 = lower level, x = upper i don't understand what i'm supposed to find/what to do

calculus
f(x) = 6x^2 8x +3 how would I find the most general antiderivative of the function. I also have to check my answer by differentiation. Would I have to find the derivative first? (I got 12x 8) What are the steps to solving a problem like this? No, don't

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

Integration by Parts
integral from 0 to 2pi of isin(t)e^(it)dt. I know my answer should be pi. **I pull i out because it is a constant. My work: let u=e^(it) du=ie^(it)dt dv=sin(t) v=cos(t) i integral sin(t)e^(it)dt= e^(it)cos(t)+i*integral cost(t)e^(it)dt do integration by

Calculus
Find the indefinite integral (integral sign) 3te^2tdt

calculus integral
Consider the integral: 21 ∫ x^3 dx 3 Use all three methods to approximate this integral with n = 3 Find the exact value of this integral

please help me calc. have test tom
d/dx integral from o to x of function cos(2*pi*x) du is first i do the integral and i find the derivative right. by the fundamental theorem of calculus, if there is an integral from o to x, don't i just plug the x in the function. the integral of the

calculus
F(x) = integral (2, x) 3t^2 (cos(t^3) +2) dt Using u(t) = t^3 , find an equivalent equation which consists of the new definite integral. Use your new expression to find F'(x) using Leibniz's Rule

Calculus
For the following integral find an appropriate TRIGONOMETRIC SUBSTITUTION of the form x=f(t) to simplify the integral. INT (x^2)/(sqrt(7x^2+4))dx dx x=?

Calculus
For the following integral find an appropriate TRIGONOMETRIC SUBSTITUTION of the form x=f(t) to simplify the integral. INT (x)/(sqrt(1918x^2+80x))dx x=?

Calc
Suppose the integral from 2 to 6 of g of x, dx equals 12 and the integral from 5 to 6 of g of x, dx equals negative 3 , find the value of the integral from 2 to 5 of 3 times g of x, dx

calculus
8). Part 1 of 2: In the solid the base is a circle x^2+y^2=16 and the crosssection perpendicular to the yaxis is a square. Set up a definite integral expressing the volume of the solid. Answer choices: integral from 4 to 4 of 4(16y^2)dy, integral from

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 xaxis from 4 to 9. For part B of our question , the surface

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)

Calculus
I have two questions, because I'm preparing for a math test on monday. 1. Use the fundamental theorem of calculus to find the derivative: (d/dt) the integral over [0, cos t] of (3/5(u^2))du I have a feeling I will be able to find the derivative easily,

Math/Calculus
How would I solve the following integral with the substitution rule? Integral of: [(x^3)*(1x^4)^5]dx Put 1x^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.

math
Generalize this to fine a formula for the integral: sin(ax)cos(bx)dx Could someone tell me what they got for an answer so I can check it to see if my answer is right. My answer: 1/2sinasinbx^21/3acosaxcosbx^3+ integral 1/3 a^2cosbx^3sinax..I'm not sure

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) =

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:

calculus
In the following problem, suppose f(x) is continuous (and differentiable) function on the interval (0,1). Suppose also that for 0 < x>please show steps

math
LEt f and g be continous functions with the following properties i. g(x) = Af(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

Calculus
Find the volume of the solid whose base is the region in the xyplane bounded by the given curves and whose crosssections perpendicular to the xaxis are (a) squares, (b) semicircles, and (c) equilateral triangles. for y=x^2, x=0, and y=0 (a) integral

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

Quick calc question
Suppose the integral from 2 to 8 of g of x, dx equals 13, and the integral from 6 to 8 of g of x, dx equals negative 3, find the value of 2 plus the integral from 2 to 6 of g of x, dx. 16 18 8 32

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

calc
find integral using table of integrals ) integral sin^4xdx this the formula i used integral sin^n xdx =1/n sin^n1xcosx +n1/n integral sin^n2 using the formula this is what i got: integral sin^4xdx=1/4sin^3xcosx+3/4 integral sin^2xdx= 1/2sinxcosx+1/2

calculus
Suppose R is the rectangle 1

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)

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

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

Calculus  Integrals
I have 3 questions, and I cannot find method that actually solves them. 1) Integral [(4s+4)/([s^2+1]*([S1]^3))] 2) Integral [ 2*sqrt[(1+cosx)/2]] 3) Integral [ 20*(sec(x))^4 Thanks in advance.

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

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]

calc check
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 that the area is ln 2 find the center of mass of the region bounded

math
suppose x S f(t) dt= x^2  2x + 1. Find f(x). 1 S = integral and 1 = lower level, x = upper i don't understand what i'm supposed to find/what to do and i didn't make any typos.

calculus
a) Let f(z) = z^2 and γ(t) = 1 + it^3, t ∈ [0,1]. i) Write out the contour integral ∫γ f(z)dz as an integral with respect to t. You do not need to evaluate this integral. ii) Evaluate the integral ∫0,1+i z^2dz iii) What is the relationship between

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

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

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

Integrals Pls help
Consider the integral: 21 ∫ x^3 dx 3 Use Left Sum, Right Sum, Midvalue Sum, and Trapezoid Rule methods to approximate this integral with n = 3 Find the exact value of this integral

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

Calculus  Center of Mass
Find the exact coordinates of the centroid given the curves: y = 1/x, y = 0, x = 1, x = 2. X = 1/Area*Integral from a to b: x*f(x)dx Y = 1/Area*Integral from a to b: [(1/2)*(f(x))^2]dx How do I find the area for this? Once I know that, is this the correct

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

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 uvintegral v du formula So first, I'm finding u and I think it's lnp.......so du is 1/p

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

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

Calculus  Integrals
Here's my first question: (FIrst part courtesy of Count Iblis) Integral of x sqrt(19x7)dx ? Write the integral in terms of functins you do know the inegral of. Rewrite the factor of x as follows: x = 1/19 (19 x) = 1/19 (19 x  7 + 7) = 1/19 (19 x  7) +

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

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

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

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=(x2)... 2. Evaluate the integral by reversing the order of integration. double integral

Calculus review
let the function h(x)= (integrand symbol from 2 to x^2)arctan (t) dt. Find h'(x). This question confused me because i know the derivative of an integral is the original function. I just need help with finding the derivative of that integral. I don't know

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

Calculus
For the following integral find an appropriate TRIGONOMETRIC SUBSTITUTION of the form x=f(t) to simplify the integral. INT x(sqrt(8x^264x+120))dx x=?

calculus
LEt f and g be continous functions with the following properties i. g(x) = Af(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

calculus
LEt f and g be continous functions with the following properties i. g(x) = Af(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

Quick calc question
Suppose the integral from 2 to 8 of g of x, dx equals 13, and the integral from 6 to 8 of g of x, dx equals negative 3, find the value of 2 plus the integral from 2 to 6 of g of x, dx. 16 18 8 32

Calculus  Integrals
I have 3 questions, and I cannot find method that actually solves them. 1) Integral [(4s+4)/([s^2+1]*([S1]^3))] 2) Integral [ 2*sqrt[(1+cosx)/2]] 3) Integral [ 20*(sec(x))^4 Thanks in advance.

calculus
Suppose f is a function of x. 1) find d/dx f^2 2)use the result to find the integral ∫ lnx/xdx. I did 1), and I got 2fdf, but im confused about number 2.

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,

Calculus
1. Find the are between the curves y=e^x and y=4x^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=4x on the left,

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.

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

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

calc
i need to find the definite integral from 0 to 2b 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 +

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

calculus II
We're doing areas by integrals now, with 2 eqns. I have a few questions. 1. Sketch the region in the xyplane defined by the inequalities x2(y^2)> 0 and 1xabs(y)>0. and find its area. Would it be best to solve for x, then graph it as x= something? Then

Calculus
Suppose f(x)=2x^2x^3 and g(x)= sin(pix/2). a) What is the exact value of the integration from 0 to 2[f(x)g(x). Find numerical approximation of this value. What does the value of this integral tell you about the areas of the regions beteen the two graph

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

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^2x1)(tanx) dx then i did a u substitution u = secx du

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^2x1)(tanx) dx then i did a u substitution u = secx du

calculus
given f(x) is continuous integral 0 to 1 f(x) f'(x)dx=0 integral 0 to 1 [f(x)]^2 f'(x) dx = 18 , find integral 0 to 1 [f(x)]^4 f'(x) dx

trig integration
s integral endpoints are 0 and pi/2 i need to find the integral of sin^2 (2x) dx. i know that the answer is pi/4, but im not sure how to get to it. i know: s sin^2(2x)dx= 1/2 [1cos (4x)] dx, but then i'm confused. The indefinite integral of (1/2) [1cos

calculus please help
what is the integral of x/(1+x^2)^2 dx This is a question of a past AP exam of calculus BC i know i have to use the substitution method where u=(1+x^2), du=2xdx. I have to find the integral but i'm just focused on the coefficient because i get a different

integrals
find value of def integral with a=2 and b=2sqrt(3) 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

Calculus
For the following integral find an appropriate trigonometric substitution of the form x=f(t) to simplify the integral. INT((4x^23)^1.5) dx x=?

Calculus
For the following integral find an appropriate TRIGNOMETRIC SUBSTITUTION of the form x=f(t) to simplify the integral. INT((4x^23)^1.5) dx x=?

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

Calculus
online class and I don't know what to do so I posts. Any help is great.Thank you Convert the integral [0,1]∫ [0,√(1x^2 y^2)]∫𝑧√(x^2 +y^2 +z^2)dz dy dx into anequivalent integral in spherical coordinates and evaluate the integral.

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

calculus
evaluate integral or state that it is diverges integral oo, 2 [2/(x^21)] dx  integral oo, 2 [2/(x^21)] dx Through partial fractions, I came up with lim [ln(x1)ln(x+1)] b, 2 b>oo I get (ln(3)0)(oooo)). The

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

Calculus
Suppose the integral from 2 to 6 of g of x, dx equals 12 and the integral from 5 to 6 of g of x, dx equals negative 3 , find the value of the integral from 2 to 5 of 3 times g of x, dx

Calculus
Suppose the total area under the curve y=x^2mx+1 from 0 to 5 is 11.3024. Find m. I know that this means that i need to find the integral of the absolute value of x^2mx+1 from 0 to 5 and set it equal to 11.3024, but I am not sure where to go from there.

def integrals
find value of def integral with a=2 and b=2sqrt(3) 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