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

F(x) = sin ([tex]\int[/tex]0 to x sin ( [tex]\int[/tex] 0 to y sin^3(u) du) dy )

find F'(x)

2. Relevant equations

FTC

3. The attempt at a solution

Is the answer

cos ([tex]\int[/tex]0 to x sin ( [tex]\int[/tex] 0 to y sin^3(u) du) dt ) sin( [tex]\int[/tex] 0 to x sin^3(u) du) dy ) sin^3(x)?

because when you differentiate the integral, the function you get becomes with respect to the boundary variable and so the last terms become with respect to x and I have to differentiate them as well?

([tex]\int[/tex]0 to x sin ( [tex]\int[/tex] 0 to y sin^3(u) du) dy ) this becomes sin ( tex]\int[/tex] 0 to x sin^3(u) du), then since the integral in the argument is with respect to x, I must differentiate that as well to get sin^3(x)

thanks

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# Homework Help: Should be easy integration

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