Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2010MathematicsDefinite Integration

The value of the integral _ / 2 ^ 3 / 2 [ x] d x , where [.] denotes the greatest integer function, is

Options

  1. A2
  2. B- 2
  3. C0

Correct answer

B. - 2

Step-by-step solution

_ / 2 ^ 3 / 2 [ x] d x= _ / 2 ^ [ x] d x+ _ ^ 3 / 2 [ x] d x= _ / 2 ^ 0 d x+ _ ^ 3 / 2 (-1) d x=-[x]_x^ 3 / 2 =- ( 3 2 - )=- 2

Practice Definite Integration on Quantrex Academy →

More from Definite Integration

₀^1 2 x+5 x^2+3 x+2 ~d x= 2025₀^1 x^ 5 / 2 (1-x)^ 3 / 2 ~d x= 2025_ n [ 1 n^2 ^2 1 n^2 + 2 n^2 ^2 4 n^2 + 3 n^2 ^2 9 n^2 + + 1 n^2 ^2 1 ]= 2025₀^1 x Sin ⁻¹ x d x= 2025_ - 2 ^ 2 (x-[x]) d x= 2025₀^2 x^2(2-x)^5 d x= 2025If f(x)= Max x^3-4, x^4-4 , and g(x)= Min x^2, x^3 , then _ -1 ^1(f(x)-g(x)) d x= 2025_ n 2 n [ 2 n + 2 2 n + 3 2 n + + 2 ]= 2025 Full Definite Integration list All Manipal MET PYQs