Question

\[\int\limits_{- \pi/2}^{\pi/2} \sin\left| x \right| dx\]  is equal to

Options

•  1

• 2

• − 1

• − 2

Answer 1

2 

\[\int_{- \frac{\pi}{2}}^\frac{\pi}{2} \sin\left| x \right| d x\]

\[ = - \int_{- \frac{\pi}{2}}^0 \sin x\ dx + \int_0^\frac{\pi}{2} \sin x\ dx\]

\[ = - \left[ - \cos x \right]_{- \frac{\pi}{2}}^0 + \left[ - \cos x \right]_0^\frac{\pi}{2} \]

\[ = 1 - 0 - 0 + 1\]

\[ = 2\]