First slide

Evaluation of definite integrals

Question

The value ,of $\int_{0}^{\sqrt{2}} [x^{2}] dx$ where [.] is the greatest integer function

Moderate

A

$2 - \sqrt{2}$
B

$2 + \sqrt{2}$
C

$\sqrt{2} - 1$
D

$\sqrt{2} - 2$

Solution

$\int_{0}^{1} [x^{2}] dx + \int_{1}^{\sqrt{2}} [x^{2}] dx = \int_{0}^{1} 0 dx + \int_{1}^{\sqrt{2}} 1 dx = (\sqrt{2} - 1)$

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