∫ 0 3 x d x = _ _ _ _ _ _ , where [ x ] is greatest integer function

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Question: Answered & Verified by Expert

\int_{0}^{3} [x] d x =______,

where

[x]

is greatest integer function

MathematicsDefinite IntegrationMHT CETMHT CET 2017

Options:

A $3$
B $0$
C $2$
D $1$

Solution:

1057 Upvotes Verified Answer

The correct answer is:

3

\int_{0}^{3} [x] d x = \int_{0}^{1} 0 d x + \int_{1}^{2} 1 d x + \int_{2}^{3} 2 d x

= {[x]}_{1}^{2} + 2 {[x]}_{2}^{3}

= (2 - 1) + 2 (3 - 2)

= 1 + 2

= 3

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