Question

If f'(x)'=\[\sin (\frac{ \pi e^X}{ 2 }\] and f(0)=1, then f(2)=?

Answer 1

Sorry, having a rough time trying to get this integral to something that can actually be done.

What level of math is it from? It'll help me narrow down my choices.

Answer 2

I', taking culculus

Answer 3

So, I can't come up with a good answer myself, but I found a resource that addresses this problem specifically: http://math.stackexchange.com/questions/297036/if-fx-sin-frac-pi-ex2-and-f0-1-what-is-f2

Answer 4

Well \[
f(2)-f(0) =\int\limits_0^2 f'(x)\;dx= \int\limits_0^2\sin\left(\frac{\pi e^x}{2}\right)dx
\]So since \(f(0) =1\) we can say: \[
f(2) = 1+\int\limits_0^2\sin\left(\frac{\pi e^x}{2}\right)dx
\]

Answer 5

How can u do it....I don't get the step that u did....like...why u did f(2)-f(0)

Answer 6

did u using Fundamental theorem

Answer 7

so then f(2)= 1 ...right