_-^|-|x||,dx is equal to :

Question

$\displaystyle\int_{-\pi}^\pi|\pi-|x||\,dx$ is equal to :

Accepted Answer

$$\int\limits_{ - \pi }^\pi  {\left| {\pi  - \left| x \right|} \right|dx} $$

= $$2\int\limits_0^\pi  {\left| {\pi  - \left| x \right|} \right|} dx$$ [As it is even function]

= $$2\int\limits_0^\pi  {\left( {\pi  - x} \right)} dx$$

= $$2\left[ {\pi x - {{{x^2}} \over 2}} \right]_0^\pi $$

= $${\pi ^2}$$

Solutions · 1