- #1

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## Homework Statement

[tex]d/dx[/tex] ([tex]\int[/tex][tex]^{x}_{0}[/tex] x

^{2}t

^{2}dt)

So the problem is to solve the derivative of the integral [tex]\int[/tex] x

^{2}t

^{2}dt from 0 to x.

## Homework Equations

[tex]d/dx[/tex] ([tex]\int[/tex][tex]^{x}_{a}[/tex] f(t)dt) = f(x)

## The Attempt at a Solution

I'm really unsure of how this should be computed but this was my guess:

[tex]d/dx[/tex] ([tex]\int[/tex][tex]^{x}_{0}[/tex] x

^{2}t

^{2}dt) = [tex]d/dx[/tex] ([tex]1/3[/tex]x

^{2}(x)

^{3}-([tex]1/3[/tex]x

^{2}(0)

^{3})) = [tex]d/dx[/tex] ([tex]1/3[/tex]x

^{5}) = [tex]5/3[/tex]x

^{4}

So, first I calculated the integral with respect to t and then derivated it with respect to x. But it feels wrong. I don't know how to treat the function x

^{2}t

^{2}because the variable x is both part of the function and an endpoint of the interval for integration.