_ - / 2 ^ / 2 ^2 x d x is equal to

Step-by-step solution

Let f(x)= ^2 x Now, aligned f(-x) & = ^2(-x)=( (-x))^2 & =(- x)^2= ^2 x=f(x) aligned So, f is an even function aligned & _ - / 2 ^ / 2 ^2 x=2 ₀^ / 2 ^2 x d x & [ _ -a ^a f(x) d x=2 ₀^a f(x) d x, if f is even ] & =2 ₀^ 2 1- 2 x 2 d x= [x- 2 x 2 ]₀^ / 2 & = ( 2 - 2 / 2 2 )- (0- (2 0) 2 ) aligned = ( 2 -0 )-(0-0)= 2