Find f if f′′(t)=2e^t+3sin(t), f(0)=−4, f(π)=−5.

Answer 1

f' = 2e^t - 3cost + C
f(0) = 2-3+C = -4 so C = -3
that makes f'(t) = 2e^t - 3cost - 3
Now do that again for f(t)