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$If [x] denotes the greatest integer less than or equal to x, then the value of the integral \int_{0}^{2} x^{2} [x] d x .$

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Correct option is A

∫02 x2[x]dx=∫01 x2[x]dx+∫12 x2[x]dx=∫01 x2(0)dx+∫12 x2(1)dx=0+∫12 x2dx=x3312=8−13=73

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If [x] denotes the greatest integer less than or equal to x , then the value of the integral ∫02 x2[x]dx .

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$If [x] denotes the greatest integer less than or equal to x, then the value of the integral \int_{0}^{2} x^{2} [x] d x .$