What is the Derivative of f(x) = Integral from x to x^2 t^2 dt?

[intelli]

Homework Statement

f(x) = integral from x to x^2

t^2 dt

find f ' (x) = ?
find f '(5)= ?

Homework Equations

The Attempt at a Solution

Break the integral in 2: \int_x^{x^2} t^2 dt = \int_x^{0} t^2 dt +\int_0^{x^2} t^2 dt = -\int_0^{x} t^2 dt + \int_0^{x^2} t^2 dt
Then take the derivative of both integrals using the FTC.

 

[slider142]

You don't even need to integrate the expression if you already learned the fundamental theorem of calculus (just be careful with your variables!). Where are you having difficulty?

 

[intelli]

This was my ans and it says that it is wrong
f ' (x) = -x^3/3+x^6/3

f ' ( 5 ) = 5166.666667

i also put

f ' ( x) = -x^2 + x ^ 4 and that was also wrong

 

[djeitnstine]

What are you using that says it is wrong? Is it a book? A program? Because sometimes a program requires input a special way.

 

[intelli]

What are you using that says it is wrong? Is it a book? A program? Because sometimes a program requires input a special way.

it is a program online i put the top ans on the program right but it says that both are incorrect ans for the f'(x) and f'(5)

 

[djeitnstine]

Figures, try putting your answer in different forms.

Such as (x^6)/3-(x^3)/3

and 5166.7

etc... I don't know exactly what they want, but you should experiment to see what format they accept.

 

[Cyosis]

This was my ans and it says that it is wrong
f ' (x) = -x^3/3+x^6/3

This is not true, f(x) is defined as $f(x)=\int_x^{x^2} t^2 dt=-x^3/3+x^6/3$. Now the ' means that you have to differentiate to x.

 

[djeitnstine]

This is not true, f(x) is defined as $f(x)=\int_x^{x^2} t^2 dt=-x^3/3+x^6/3$. Now the ' means that you have to differentiate to x.

good looking I didn't even see the '

 

[slider142]

This was my ans and it says that it is wrong
f ' (x) = -x^3/3+x^6/3

That is indeed incorrect. You are giving f(x), while the question asks for f'(x). Once again, note that there is no need to integrate the expression. Use the fundamental theorem of calculus.

 

[intelli]

That is indeed incorrect. You are giving f(x), while the question asks for f'(x). Once again, note that there is no need to integrate the expression. Use the fundamental theorem of calculus.

thanks a lot guys i figured it out