$\int\limits_{ - \pi }^\pi {\left| {\pi - \left| x \right|} \right|dx}$ is equal to :
Solution
$\int\limits_{ - \pi }^\pi {\left| {\pi - \left| x \right|} \right|dx}$
<br><br>= $2\int\limits_0^\pi {\left| {\pi - \left| x \right|} \right|} dx$ [As it is even function]
<br><br>= $2\int\limits_0^\pi {\left( {\pi - x} \right)} dx$
<br><br>= $2\left[ {\pi x - {{{x^2}} \over 2}} \right]_0^\pi$
<br><br>= ${\pi ^2}$
About this question
Subject: Mathematics · Chapter: Definite Integration · Topic: Properties of Definite Integrals
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