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Problem 43 Hard Difficulty

Evaluate the integral.

$ \displaystyle \int^{\pi}_0 f(x) \,dx $ where $ f(x) = \left\{
\begin{array}{ll}
\sin x & \mbox{if $ 0 \le x < \pi/2 $}\\
\cos x & \mbox{if $ \pi/2 \le x \le \pi $}
\end{array} \right.$

Answer

$$
0
$$

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Video Transcript

The first thing we know is that we can split the integral. We know there's a property of inter girls that allows us to split them up into two, which makes it easier to them plug in and souls, which means we cannot plug in to get we end up with simply zero.