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The value of $\int\limits_0^2[x^2-1]dx$, where [x] denotes the greatest integer function, is given by: |
$3-\sqrt{3}-\sqrt{2}$ 2 1 None of these |
$3-\sqrt{3}-\sqrt{2}$ |
$I=\int\limits_0^2[x^2]dx-\int\limits_0^21.dx=\int\limits_0^10dx+\int\limits_1^{\sqrt{2}}1dx+\int\limits_{\sqrt{2}}^{\sqrt{3}}2dx+\int\limits_{\sqrt{3}}^23dx-2=3-\sqrt{3}-\sqrt{2}$ |
