Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202123 Sep 2021Morning ShiftMathematicsDefinite IntegrationActual

₀^4 x[x] d x=( where [x] denotes greatest integer function not greater than x )

Options

  1. A17
  2. B24
  3. C21 2
  4. D33 2

Correct answer

A. 17

Step-by-step solution

Let I= ₀^4 x[x] d x aligned & I= ₀^1(0) d x+ ₁^2 x d x+ ₂^3 2 x d x+ ₃^4 3 x d x & = [ x^2 2 ]₁^2+ [ 2 x^2 2 ]₂^3+ [ 3 x^2 2 ]₃^4 & = 1 2 (4-1)+(9-4)+ ( 3 2 )(16-9)= 3 2 +5+ 21 2 =17 aligned

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 MHT CET PYQs