Q67 / 125 · BITSAT 2017 · Mathematics

The expression ∫0nxdx∫0nxdx, where x and x are integral and fractional part of x and n∈N, is equal to

  • A
    1n-1
  • B
    1n
  • C
    n
  • Correct answer
    D
    n-1

Solution

We have, ∫0nxdx

=∫010dx+∫121dx+∫232dx+…+∫n-1nn-1dx

=12-1+23-2+34-3+……+n-1n-n-1

=1+2+3+….+n-1=nn-12

and ∫0nxdx=∫0nx-xdx=n2

∴ ∫0nxdx∫0nxdx=n-1

Hence, the correct answer is option: 'D'.

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