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Numerade Educator

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Problem 45 Hard Difficulty

Find $ f $.

$ f"(x) = e^x - 2\sin x $, $ \quad f(0) = 3 $, $ \quad f(\pi/2) = 0 $

Answer

$$
f(x)=e^{x}+2 \sin x-\frac{2}{\pi}\left(4+e^{\frac{\pi}{2}}\right) x+2
$$

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Video Transcript

So for this problem were given F double crime of X. And our goal is to find fx. So if F double prime of X is given to us as a L e x minus two sine X. And we're going to take the anti derivative of this to get F prime. You can give us E d x times, uh E X plus two code syntax, plus some constancy. But we can find with this constant is going to be 12 or pie times or plus each of the power tube. Yeah, you get a result. And then um for F of crime we take our F of X, take the anti derivative again we get E X um plus two Synnex. Thanks. This whole thing is a constant. So we just put X at the end of it and then we have plots another constant, solving with the initial condition we get plus two. This is the final answer.