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Maths Calculus Derivative Integral - Urgent Please

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Maths Calculus Derivative Integral - Urgent Please
Use 2nd Fundamental Theorem of Calculus to find derivative of f(x) = integral of 2x^2 (at the top) to x-5 (at the bottom) of square root of Sin(x)dx

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!!!

Calculus
If I have a function f(x), and am given its derivative, f'(x): may I take it as a given that f(x) is an integral of f'(x). My reasoning is that 'undoing' the derivative gives me the derivative. Eg is 1/3x^3 an integral of x^2? Thanks.

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 how to post integral ...

Calculus Help Please Urgent!!!
Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places. integral from o to pi/2 (2cos^3(x))dx , n = 4 M4 = ?????? Thanks!!!

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 problem is cos*2*pi*) is ...

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 problem is cos*2*pi*) is ...

Calculus prince@18
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 how to post integral ...

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 integral from 0(on the ...

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 do the derivative ...

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, I'm just having trouble...

calculus
Find the length of the arc formed by y = (1/8)(4x^2-2ln(x)) from x=4 to x=8. I found the derivative of the function and got y'= x-(1/4x) Where I'm lost now is after plugging it into the arc length equation: integral of sqrt(1+(x-(1/4x))^2). Squaring the derivative yields me ...

Math
Use 2nd Fundamental Theorem of Calculus to find derivative of f(x) = integral of 2x^2 to x-5 of square root of Sin(t)dt. Please help.

Calculus
1) Find the derivative with respect to x of Integral from 1 to X^3 of sqrt( 1 + t²) dt I got sqrt( 1 + X^6) * 3x². Is that right? 2) Integral from 0 to pi/2 of Xcos(X²)dx

AP calculus
∫[0,x^(3),(t)/√(1+t^(3)),] Find the derivative of the integral. A. (3(x^3))/((1+(x^9))^0.5) B. (x^3)/((1+x^9)^0.5) C. (3x^3)/((1+x^3)^0.5) D. (5x^3)/((1+x^6)^0.5) E. (3x^5)/((1+x^3)^0.5) I think the answer is A. Can you check my answer please?

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 Then, I think dv = p...

calculus(urgent pls)
Integral of 1/[x^2(1+x^2)]

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 integral from 0(on the ...

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 integral from a to a of...

Calculus
Find the anti-derivative of the integral [(7t^2+6t-15)/t^4]dt

Calculus
Find the derivative of the integral from x to 6 of ln(1 + t^2). My answer is -ln(1+x^2).

Calculus AB (AP)
Hi, I have a calculus test tomorrow and I understand how to complete all of the problems, but I am unsure behind the reasoning of taking two derivatives. Can someone please explain the following: 1. g(x)=e^(f(x)) g'(x)=e^(f(x))f'(x) 2. f(x)=Integral from 0 to 3x of the square ...

Calculus
Given the equation xy = 2, set up an integral to find the length of path from x = a to x = b and enter the integrand below. I did the integral from b to a and set it equal to the sqrt(1+4/x^4), because I found y to equal 2/x and the derivative to be -2/x^2, but I think I am ...

Calculus
Find the derivative of Integral from -5 to sin(x) of cos(t^3)+t

calculus
Find the derivative d/dx of the integral from x to a of cos(sin(t)) dt

AP calculus
∫[0,x^(3),(t)/√(1+t^(3)),] Find the derivative of the integral. A. (3(x^3))/((1+(x^9))^0.5) B. (x^3)/((1+x^9)^0.5) C. (3x^3)/((1+x^3)^0.5) D. (5x^3)/((1+x^6)^0.5) E. (3x^5)/((1+x^3)^0.5)

Calculus
Find the anti-derivative of the integral (7tan^2x+12)dx

Calculus
Find the anti-derivative of the integral [3sqrt(x)(2x^2-4)]dx

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) Integral d/da [t^(a)]dt = d/...

Calculus(URGENT PLS!!!)
Find the integral of (e^cosx)sinx

calculus help
find the derivative of the function. integral cos(x) to sin(x) ((ln(8+3v))dv)

calculus help
find the derivative of the function integral from cosx to sinx (ln(8+3v)dv)

Calculus
Find the derivative of the integral from x^3 to 5 of cosk/(k^2+2). My answer is ((-cos(x^3)(3x^2))/(x^6+2).

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. next, let u = sqrt x + 1 ...

calculus urgent
If you are given a graph of a function, how do you draw the derivative?

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

calculus -- PLEASE HELP!
1. Describe how you could approximately find the total number of particles in a rectangular box that is 2m x 2m x 3m by making no more than 12 samples. 2. You know the following facts about a function f(x): The derivative of f(x) is 6x + 4. The integral of f(x) from 1 to 3 is ...

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.

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

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 (x^2)^2 from 0 to 2=32/5...

calculus
What is the definite integral from 0 to x of 1/(4 + t + 3t^2) dt? For starters, what is the anti-derivative and how did you find it? I think I could take it from there.

calculus help
find derivative of integral( t sint dt) upper limit 1+2x, lower limit 1-2x Show step by step please! Thank you

maths help needed!(urgent)
find the equation of the tangent to y=x-(a^3/x^2) at the point (a,0) how to i work this out??can someone please show me how to do it step by step?thanks!!! Take the dervative of y y= x- a^3 x^-2 y'=1+2a^3/x^3 so the equation for the tangent is y= mx + b where m is y' above ...

Calculus 2 (Differential Equation)
How would you solve the following problem explicitly? Sqrt(1-y^2) dx - sqrt(1-x^2) dy I separated the x and y terms and got: Integral of 1/sqrt(1-x^2) dx = Integral of 1/sqrt(1-y^2) dy I was wondering how would you take the anti-derivative of each function. I believe we are ...

CALCULUS! PLEASE HELP URGENT!
Which of the following functions have a derivative at x=0? I. y= absolute value(x^3-3x^2) II y= square root(x^2+.01)- absolute value (x-1) III y= e^x/cosx

Calculus1
find the derivative using fundamental theorem of calculus integral of sin^3tdt from e^x to 0

Calculus Please check
Please check my answers and let me know if I did something wrong. Thank you! Find the partial derivative of x, and the partial derivative of y, then the partial derivative of x (1,-1), and the partal derivative of y (1,-1). f(x,y) = x^4 y^2 -x here is what I got @f/@x = 3x^3 y...

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 of revolution ...

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 answer for that part ...

Math
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function h(x)=integral [2,1/x]sin^4t dt

Calculus
Integration with U-Substitution Integral of [x/sqrt(x+1)] dx I'm getting confused with how to deal with the x when I find the derivative of (x+1) because they don't match.

Calculus (double integral) PLEASE HELP!
Evaluate double integral ln((x-y)/(x+y)) dy dx where the double integral region is the triangle with vertices (1,0),(4,3), (4,1). Hint: use a transformation with the Jacobian.

MATHS! URGENT!
describe how each sequence is generated and write down the next two terms: a) 40 41 43 46 50 55 b)90 89 87 84 80 75 c)1 3 7 13 21 31 d) 2 6 12 20 30 42 PLEASE HELP its urgent!

integral Calculus
Please help me with this integral problem: ʃ x^2(a^2-x^4)^2dx please help..thanks alot:)

calculus
Please help with this. I need the first derivative of f(x)=4(x+squareroot (x(8-x)) and then the second derivative of this to show by the second derivative test that it is a local maximum. This is difficult to put into form here and I hope I have got it right. Many thanks.

Calculus
Evaluate the integral: the integral of [5e^(2t)]/[1+4e^(2t)]dt. I used u sub and let u=e^2t and got 5/2arctan(e^2t)+C. But this answer is incorrect. Please help. Thanks

Calculus
Evaluate the integral: the integral of [5e^(2t)]/[1+4e^(2t)]dt. I used u sub and let u=e^2t and got 5/2arctan(e^2t)+C. But this answer is incorrect. Please help. Thanks

Calculus
Use a symbolic differentiation utility to find the derivative of the function g(x)=xã((x^2)+1). Use the utility to graph the function and is derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeroes of the graph of ...

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 f(x)=arctan->f'(x)=1...

Calculus I
Find the derivative of y=ln((1+e^x)/(1-e^x)) I know that the derivative of y=ln(1+e^x) would be (e^x)/(1+e^x), but I'm not sure what to do with the 1-e^x on the bottom here. Can someone help please? Thanks!

Calculus
In the interval (0 is less than or equal to x which is less than or equal to 5), the graphs of y=cos(2x) and y=sin(3x) intersect four times. Let A, B, C, and D be the x-coordinates of these points so that 0<A<B<C<D<5. Which of the definite integrals below ...

calculus
if f(x)= the integral of lntdt from sqrt(x) to 2, what is f'(x)? Do you solve the integral first then derive it? And if so, wouldn't that just give you the function? Please help

Calculus Please Help2
Evaluate the integral by using substitution. Use an upper-case "C" for the constant of integration. integral x^5((x^6-2)^10)dx ty

Calculus
Use derivative formulas to find the derivative of the function. please show your work h(x)=10^3-25x^6+3x^15

calculus
Please help with this. I submitted it below and was asked to clarify by Henry (hope this is clearer and thank you). I need the first derivative of f(x)=4(x+ sqrt (x(8-x)).And then the second derivative of this to show by the second derivative test that it is a local maximum. ...

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 by parts. but i can't ...

Calculus
Find the derivative of the function using the definition of a derivative. F(x)=squareroot(1-3x) Please show work for understanding, thank you! :)

Calculus
I'm having some issues with computing this indefinite integral. I don't know how to even begin. Please help! (let S be the symbol for the integral) S (square root (x)+e^-3x) dx

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 sinx*cosx*dx from -...

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

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 -4 to 4 of (16+y^2)dy...

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!

Calculus - repost
Find the derivative of F(x)= integral from -2 to x of sqrt(t^3+8)dt? My answer: sqrt(x^3+8)? Is this right?

Calculus
Find the derivative of the integral from 2 to 5x of (sqrt(1 + u^2))/u. My answer: (sqrt(1 + 25x^2)/5x) * 5

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 integral from 0(on the ...

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

differential equations
the directions are to determine whether or not the equation is exact if so then solve it. the question is (x-y^3+ysinx)dx = (3xy^2+2ycosx)dy i solve and i got that it is exact because My is -3y^2+2ysinx and Nx is -3y^2+2ysinx since m and n are equal then they are exact then i ...

Integral calculus
You have not proved to me that the Integral of lnsinx w.r.t.x from 0 to pi/2 is equal to:Integral of lnsinx w.r.t.x from 0 to pi/4 plus Integral of lncosx w.r.t.x from 0 to pi/4.

Calculus--> bobpursley
How do you get m=0? from taking the second derivative? does c=1? Can you check my work on how I get the derivative of R=M^2(c/2-m/3) NEXT R=1/2(CM^2)-1/3(M^3) NEXT dR/dM=CM-M^2. I checked in the back, and that was the answer for the first part of the equation. Isn't the ...

Calculus
(x+y)^4 can be expanded starting at x^4*y^0 and taking the sum of the products of the derivative of the x term and the integral of the y term? Why does this work?

Calculus
Find the derivative of F(x)= integral from -2 to x of sqrt(t^3+8)dt? My answer: sqrt(x^3+8)?

calculus
Please help with this. I submitted it below but no one responded. I need the first derivative of f(x)=4(x+ then the square root to include (x(8-x)), then close bracket.And then the second derivative of this to show by the second derivative test that it is a local maximum. This...

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.

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.

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 of f(x)dx in terms of ...

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 of f(x)dx in terms of ...

MATH urgent
Hello!! 1. find the third derivative of f(t)=(t-1)/(t+1) 2. y= x^(x^2) ; dy/dx please help! thank you!

Calculus
Evaluate the integral. 1/2 integral e^(t/2) (I'm not sure what the 1/2 on the left of the integral symbol means.)

Calculus II
y = *The Integral Of sin(4e^t)dt* a = 0 b = ln(2x) I'm supposed to find the derivative of y with respect to x. Except I just can't find the right answer.

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 answer in the back ...

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)

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 converges CONFUSE: how would...

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 N-->infinity? Does ...

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 N-->infinity? Does ...

Calculus
use te fundamental theorem of calculus to evaluate the integral Integral [0, pi/3] sin^2(x)dx I'm confused on what F(x) should be

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 [1-cos (4x)] dx, but then i'm confused. The indefinite integral of (1/2) [1-cos (4x)] is (x/2) - (1/2...

Calculus
for the function F(t)=ln(t^2), let f(t)=F'(t). Write the integral from a to b of f(t) dt and evaluate it with the fundamental theorem of calculus. the integral from 1 to 3 ___ dt= __

Calculus
What is the integral or e^(-x)? What is the derivative of - e-x ?

Calculus
Evaluate the improper integral or state that it diverges: integral from -inf to inf (2xe^-x) dx. Please help!

Calculus - derivatives
Okay, I want to find the derivative of (x^x)^(x^x)... Well, I already went through the process of finding the derivative of just x^x (I used ln to do this). This is what I found... dy/dx = x^x(lnx+1) So now I want to find the derivative of (x^x)^(x^x) (using ln). This is what ...

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