The value of $\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}}(sin|x|-cos|x|)dx$

-1 2 0 1

0

The correct answer is Option (3) → 0 $\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}}(\sin|x|-\cos|x|)dx$ $=2\int\limits^{\frac{\pi}{2}}_{0}\sin x-\cos xdx$ $=2\left[-\cos x-\sin x\right]^{\frac{\pi}{2}}_{0}$ $=2[0-1+1+0]=0$