(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[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.

2. Relevant equations

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

3. 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.

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# Homework Help: Differentiating integrals

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