PYQ Vault
EbooksTutor

Integral of x times [x] or x^2 times [x], split at the integers

This type of question, asked 4 times: 16 May 2023 S2, 11 Apr 2026 S1, 20 Apr 2026 S1, 13 May 2026 S1. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    16 May 2023 S2

    126
    If [x][x] denotes the greatest integer function, then ∫05x2[x] dx=\int_0^5 x^2[x]\,dx =

    Tap an option to check your answer.

  2. Question 2

    11 Apr 2026 S1

    81
    If [⋅][\cdot] denotes the greatest integer function, then ∫14x[x] dx\displaystyle\int_1^4 x[x]\,dx is equal to

    Tap an option to check your answer.

  3. Question 3

    20 Apr 2026 S1

    81
    If [x][x] denotes the greatest integer less than or equal to xx, then the value of the integral ∫02x2[x] dx\int_0^2 x^2[x]\,dx is equal to

    Tap an option to check your answer.

  4. Question 4

    13 May 2026 S1

    81
    Let In=∫nn+1x[x] dxI_n = \int_n^{n+1}x[x]\,dx, where [x][x] denotes greatest integer function and n∈Nn \in N. If In=18I_n = 18, then the value of nn is...

    Tap an option to check your answer.