Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main201815 Apr 2018Morning ShiftMathematicsDefinite IntegrationActual

The value of the integral _ - 2 ^ 2 ^4 x (1+ ( 2+ x 2- x ) ) d x is

Options

  1. A3 16
  2. B0
  3. C3 8
  4. D3 4

Correct answer

C. 3 8

Step-by-step solution

Let aligned I &= _ - 2 ^ 2 ^4 x (1+ ( 2+ x 2- x ) ) d x .(1) I & .= _ - 2 ^ 2 ^4(-x) ) (1+ ( 2+ (-x) 2- (-x) ) ) d x &= [ _a^b f(x) . d x= _a^b f(a+b-x) d x ] aligned aligned &= _ - 2 ^ 2 ( ^4 x ) (1+ ( 2- x 2+ x ) ) d x &= _ - 2 ^ 2 ^4 x (1- ( 2+ x 2- x ) ) d x .(2) aligned After adding equation (1) and (2) we get, aligned &2 I=2 _ - 2 ^ 2 ^4 x d x &2 I=4 ₀^ 2 ^4 x d x &I=2 ₀^ 2 ^4 x d x= 3 2 1 2 2 2 = 3 8 & [ By Gamma function] aligned

Practice Definite Integration on Quantrex Academy →

More from Definite Integration

The value of the definite integral ₀² 1 3^ x+3 2 , dx is 2026The value of the integral ₀² x(x^2+x+1) ( x+1 )( x^4+x^2+1 ) , dx is equal to: 2026If _ /6 ^ /4 ( (x- 3 ) (x+ 3 )+1 )dx = _e( 3 -1) , then 9 ^2 is equal to ________. 2026Let A = bmatrix 1 & 3 & -1 2 & 1 & 0 & 1 & -1 bmatrix be a singular matrix. Let f(x) = ₀^x (t^2 + 2t + 3) ,dt , x [1, ] . If M and m are respectively the maximum and the minimum va 2026Let f: R R be such that f(xy) = f(x)f(y) , for all x, y R and f(0) 0 . Let g: [1, ) R be a differentiable function such that x^2 g(x) = ₁^x (t^2 f(t) - tg(t)) ,dt . Then g(2) is eq 2026The value of the integral _ -1 ¹ ( x^3 + |x| + 1 x^2 + 2|x| + 1 ) dx is equal to : 2026The value of the integral _ - /4 ^ /4 ( 32 ^4 x 1 + e^ x )dx is: 2026Let (2^ 1-a + 2^ 1+a ) , f(a) , (3^a + 3^ -a ) be in A.P. and be the minimum value of f(a) . Then the value of the integral _ _e( -1) ^ _e( ) dx (e^ 2x - e^ -2x ) is : 2026 Full Definite Integration list All JEE Main PYQs