Question

Integrate

Answer 1

\[\LARGE \int\limits_{-\frac{\pi}{2}}^\frac{\pi}{2} \sin|x|+\cos|x|\]

Answer 2

Attempt:
\[\LARGE \int\limits_{\frac{-\pi}{2}}^0 \cos x- \sin x + \int\limits_{0}^{\frac{\pi}{2}} \sin x+ \cos x\]

Answer 3

the nature will break at x=0 for the mod function so i separated the integrals

Answer 4

and from -90 to +0 sin is -ve and cos is +ve and on the other interval both are +ve

Answer 5

gives 2 as the answer which is wrong..

Answer 6

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Answer 7

Check the derivatives of the trigometric functions then it will be easy for u to solve.

Answer 8

the function is evidently even
so you can compute
\[2\int_0^{\frac{\pi}{2}}\sin(|x|)+\cos(|x|)dx\] and since both sine and cosine are positive on that interval, it should be the same as \[2\int_0^{\frac{\pi}{2}}\sin(x)+\cos(x)dx\]

Answer 9

what was wrong with my method if I don't apply the property?