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