∫ |π - | x || dx, x∈[-π, π] is equal to : (i) π^2 (2) 2 π^2 (3) √2 π^2 (4) π^2/2 ​

Question

\(\int \limits_ {-π}^{π}\)|π - | x || dx is equal to :

(1) π² 

(2) 2 π²

(3) √2 π²

(4) π²/2

Answer 1

(1) π² ​​​​​​​

 \(\int \limits_ {-π}^{π}\)|π - | x || dx 

= 2 \(\int \limits_ {0}^{π}\)|π -  x | dx 

=  2 \(\int \limits_ {0}^{π}\)(π -  x ) dx