∫$$02$$ $$x2$$[x]$$dx=$$∫$$01$$ $$odx+$$∫$$12$$ $$x2dx=x332=83$$−$$13=73=2.3330$$

Evaluation of definite integrals

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$\int_{0}^{2} x^{2} [x] d x =$

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$\begin{array}{l} \int_{0}^{2} x^{2} [x] d x = \int_{0}^{1} o d x + \int_{1}^{2} x^{2} d x = {(\frac{x^{3}}{3})}^{2} \\ = \frac{8}{3} - \frac{1}{3} = \frac{7}{3} = 2.3330 \end{array}$

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