If f'(x) = \sin\left(\frac{\pi}{2}e^x\right) and $f(0) = 1$ then $f(2) =?$
I'm currently studying for my calculus exam and came across this multiple choice question. I have tried to do $u$ substitution to get $f(x) + c$. And then to just plug in the values. I have been dwelling on this for half an hour now either I'm doing it right and getting the answer wrong I have the wrong approach. Would someone please be kind enough to show a step by step guide for questions like these in general ( so its useful for other people as well).
The choices are:
- A $-1.819$
- B $-0.843$
- C $-0.819 $
- D $0.157$
- E $1.157 $