Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main201910 Apr 2019Morning ShiftMathematicsDefinite IntegrationActual

l i m n → ∞ ( n + 1 ) 1 / 3 n 4 / 3 + ( n + 2 ) 1 / 3 n 4 / 3 + . . . . . + ( 2 n ) 1 / 3 n 4 / 3 is equal to

Options

  1. A3 4 ( 2 ) 4 / 3 - 3 4
  2. B4 3 ( 2 ) 3 / 4
  3. C4 3 ( 2 ) 4 / 3
  4. D3 4 ( 2 ) 4 / 3 - 4 3

Correct answer

A. 3 4 ( 2 ) 4 / 3 - 3 4

Step-by-step solution

The given limit can be written as l i m n → ∞ 1 n 1 + 1 n 1 3 + 1 + 2 n 1 3 + … . + 1 + n n 1 3 = l i m n → ∞ 1 n ∑ r = 1 n 1 + r n 1 3 = ∫ 0 1 ( 1 + x ) 1 / 3 d x = 1 + x 4 3 4 3 0 1 = 3 4 ( 2 4 / 3 – 1 ) = 3 4 . 2 4 / 3 - 3 4

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