FTC help

[jm2hill]

Hi I have a question that goes like this:

I hope its clear not sure if there's a way to post it nicely

Find f''(x),
given: \[f(x) = \int_{0}^{x} g(t) dt\] and \[g(t) = \int_{0}^{cos(t)} u^2 du\]

The way I've approached it is to use FTC1 + chain rule on g(t) so solve for f'(x) giving you:

\[f'(x) = \int_{0}^{x} -cos(t)^2 * sin(t) dt\]



then using FTC1 again to solve for f''(x)

giving you: \[f''(x) = -cos(x)^2 * sin(x)\]

Let me know if I'm on right track!

Thanks

 

[fcabanski]

The first step is to write g(t) as a simple function (not an integral). Solve that integral first.

Also, look at the Second Fundamental Theorem of Calculus:

http://mathworld.wolfram.com/SecondFundamentalTheoremofCalculus.html