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  4. If [x] is the greatest integer function not greater than x then ∫ limits08[x] d x is equal to

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Q. If $[x]$ is the greatest integer function not greater than $x$ then $\int\limits_{0}^{8}[x] d x$ is equal to

KCETKCET 2022Integrals

Solution:

$\int\limits_{0}^{8}[x] d x=1+2+3+\ldots .+7$
$=\frac{7(7+1)}{2}=28$