Consider the function.
Find F''(2)
(thanks in advance..
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these are just using the second fundamental theorem of calculus: in a nutshell it says:
if $\displaystyle f(x) = \int_c^{g(x)}f(t)~dt$, then $\displaystyle f'(x) = f(g(x)) \cdot g'(x)$
where $\displaystyle c$ is any constant and $\displaystyle g(x)$ is some function of $\displaystyle x$.
Use this to find $\displaystyle f'(x)$. then to get $\displaystyle f''(x)$, just take the regular derivative of $\displaystyle f'(x)$
Can you continue?
the point of my first post was showing that you do not have to do any integrals here. just use the fundamental theorem of calculus that i posted. do you understand what the theorem says? all you need for this problem is derivatives, and that's only because we are going to the second derivative. DO NOT EVALUATE ANY INTEGRALS.
that would not work...