Definite Integration Question 62
Question 62
- The integral $\int_{0}^{1.5}\left[x^{2}\right] d x$, where [.] denotes the greatest function, equals
$(1988,2 M)$
Match the Columns
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Solution:
- $\int_{0}^{1.5}\left[x^{2}\right] d x=\int_{0}^{1} 0 d x+\int_{1}^{\sqrt{2}} 1 d x+\int_{\sqrt{2}}^{1.5} 2 d x$
$$ \begin{aligned} & =0+[x]{1}^{\sqrt{2}}+2[x]{\sqrt{2}}^{1.5} \ & =(\sqrt{2}-1)+2(1.5-\sqrt{2}) \ & =\sqrt{2}-1+3-2 \sqrt{2} \ & =2-\sqrt{2} \end{aligned} $$
