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Maths Definite Integral and Area Under Curves General Subjective Type

Published on: August 13, 2026

Prove that: = x [x] – [x] {[x] +1}

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Sol. Let k be an integer such that k ≤ x < k + 1. Then,

= +

= + + ..... + +

= +

= + k(x –k)

= (1 + 2 + ....+ k –1) + k (x –k)

= + kx – k 2

. = kx –

= [x] x –

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