Let $ [\cdot] $ denote the greatest integer function. Then how to evaluate the integral $$I=\int_0^2 [x^2]dx?$$
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Please help to edit and solve – DINESH BISWAS Apr 19 '20 at 03:56
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Please check that I haven't altered the meaning of your question. – Reveillark Apr 19 '20 at 03:59
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Hint:
$$\int_0^2\lfloor x^2\rfloor dx=\int_0^1 0dx+\int_1^\sqrt21dx+\int_\sqrt2^\sqrt3 2dx+\int_\sqrt3^23dx$$
J. W. Tanner
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Integrals are additive on intervals; I chose intervals where $\lfloor x^2\rfloor$ is constant, so the integrals are easy to evaluate – J. W. Tanner Apr 19 '20 at 04:19