$\mathop \smallint \limits_0^{\sqrt 2 } \,\,\left[ {{x^2}} \right]\,\,dx$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

\int \limits_0^{\sqrt 2 } \,\,\left[ {{x^2}} \right]\,\,dx

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Correct option: C

\sqrt 2 - 1

Option C (√2 - 1) is correct because the integral of the greatest integer function [x²] from 0 to √2 can be split into two integrals, one from 0 to 1 where [x²] = 0 and another from 1 to √2 where [x²] = 1.

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