The value of ₀^ 4 x d x+ ₀^ 4 x d x is equal to

Step-by-step solution

aligned & ₀^ 4 x d x+ ₀^ 4 x d x & = ₀^ 4 ( x + x ) d x aligned aligned & = ₀^ 4 ( x x + x x ) d x & = ₀^ 4 x+ x x x d x aligned aligned & = 2 ₀^ 4 ( x+ x) ( 1- ( ^2 x+ ^2 x-2 x x ) ) d x & = 2 ₀^ 4 ( x+ x) 1-( x- x)^2 d x aligned Put x - x = t ( x + x ) d ~d = dt When x=0, t=-1 and x= 4 , t=0 . aligned & = 2 _ -1 ^0 1 1- t ^2 dt = 2 ( ⁻¹ t )_ -1 ^0 & = 2 [ ⁻¹(0)- ⁻¹(-1) ] & = 2 [0- ( - 2 ) ]= 2 aligned