Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
99 Percentile Qs Bank for JEE MainMathematicsDefinite Integration

If ∫ 0 π log ( sin x ) d x = 8 k , then ∫ 0 π / 4 log ( 1 + tan x ) d x =

Options

  1. Ak
  2. B- k
  3. Ck 2
  4. D4   k

Correct answer

B. - k

Step-by-step solution

Let I = ∫ 0 π / 4 log ( 1 + tan x ) d x Using property of integration ∫ 0 a f ( x ) d x = ∫ 0 a f ( a - x ) d x ⇒ I = ∫ 0 π 4 log 1 + tan π 4 - x d x ⇒ I = ∫ 0 π 4 log 2 1 + tan x d x ⇒ I = ∫ 0 π 4 log 2 d x - ∫ 0 π 4 log 1 + tan x d x ⇒ I = π 4 log 2 - I               ∵ I = ∫ 0 π 4 log 1 + tan x d x ⇒ 2 I = π 4 log 2 ⇒ I = π 8 log 2   &#

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 99 Percentile Qs Bank for JEE Main PYQs