What is the integral from-pi/2 to pi of xsin(|x|) ?

The integral from-pi/2 to pi of xsin(|x|) is -1+pi

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integral from-pi/2 to pi of xsin(|x|)

\int_{- \frac{π}{2}}^{π} x sin (∣ x ∣) d x

- 1 + π

Decimal

2.14159 \dots

Solution steps

\int_{- \frac{π}{2}}^{π} x sin (∣ x ∣) d x

Eliminate Absolutes

= \int_{- \frac{π}{2}}^{0} x sin (- x) d x + \int_{0}^{π} x sin (x) d x

\int_{- \frac{π}{2}}^{0} x sin (- x) d x = - 1

\int_{0}^{π} x sin (x) d x = π

= - 1 + π

What is the integral from-pi/2 to pi of xsin(|x|) ?
The integral from-pi/2 to pi of xsin(|x|) is -1+pi