Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202125 Feb 2021Evening ShiftMathematicsDefinite IntegrationActual

If I n = ∫ π 4 π 2 cot n x d x , then

Options

  1. AI 2 + I 4 , I 3 + I 5 2 , I 4 + I 6 are in G . P .
  2. BI 2 + I 4 , I 3 + I 5 , I 4 + I 6 are in A . P .
  3. C1 I 2 + I 4 , 1 I 3 + I 5 , 1 I 4 + I 6 are in A . P .
  4. D1 I 2 + I 4 , 1 I 3 + I 5 , 1 I 4 + I 6 are in G . P .

Correct answer

C. 1 I 2 + I 4 , 1 I 3 + I 5 , 1 I 4 + I 6 are in A . P .

Step-by-step solution

I n = ∫ π / 4 π / 2 cot n x d x = ∫ π / 4 π / 2 cot n - 2 x cosec 2 x - 1 d x = - cot n - 1 x n - 1 π / 4 π / 2 - I n - 2 = 1 n - 1 - I n - 2 ⇒ I n + I n - 2 = 1 n - 1 ⇒ I 2 + I 4 = 1 3 I 3 + I 5 = 1 4 I 4 + I 6 = 1 5 ∴ 1 I 2 + I 4 , 1 I 3 + I 5 , 1 I 4 + I 6 are in A . P .

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