MHT CET20243 May 2024Evening ShiftMathematicsDefinite IntegrationActual
The value of the integral _ - 2 ^ 2 (x^2+ -x +x ) x d x is equal to
Options
- A0
- B^2 2 -4
- C^2 2
- D^2 2 +4
Correct answer
B. ^2 2 -4
Step-by-step solution
Let I = _ - 2 ^ 2 [x^2+ ( -x +x ) ] x ~d x I = _ - 2 ^ 2 x^2 x ~d x+ _ - 2 ^ 2 ( -x +x ) x ~d x Let I = I ₁+ I ₂ Where I ₁= _ - 2 ^ 2 x^2 x ~d x and I ₂= _ - 2 ^ 2 ( -x +x ) x ~d x Consider aligned & I₁= _ - 2 ^ 2 x^2 x d x & =2 ₀^ 2 x^2 x d x aligned [x^2 x . is an even function ]=2 [x^2 x ~d x- d d x (x^2 ) ( x ~d x ) d x ]₀^ 2 aligned & =2 [x^2 x- 2 x x d x ]₀^ 2 & =2 [x^2 x-2 x x d x ]₀^ 2 aligned =2 [x^2 x-2 (x(- x)- (- x) d x ) ]₀^ 2 aligned & =2 [x^2 x+2 x x-2 x ]₀^ 2 & =2 [ ^2 4 2 +2 2 2 -2 2 . aligned .-0^