₀^ / 4 x+ x 3+ 2 x d x is

Step-by-step solution

₀^ / 4 x+ x 3+ 2 x d x= ₀^ / 4 ( x+ x) 4-(1- 2 x) d x= ₀^ / 4 ( x+ x) 4-( x- x)² d x Put t=( x- x)d t=( x+ x) d x= _ -1 ⁰ d t (4-t² ) = _ -1 ⁰ dt (2+ t )(2- t ) = 1 4 _ -1 ⁰ [ 1 2+t + 1 2-t ] d t= 1 4 [ (2+t)- (2-t)]_ -1 ⁰ aligned &= 1 4 [ ( 2+ t 2- t ) ]_ -1 ⁰ &= 1 4 [ (1)- ( 1 3 ) ] &= 1 4 3 aligned