Question

Evaluate:

${\int }_0^{\sqrt{2}}{x}^{2}dx$

• A. $2-\sqrt{2}$
• B. $2+\sqrt{2}$
• C. $\frac{2\sqrt{2}}{3}$
• D. $\frac{4}{3}$

Answer 1

Answer: (C)

$\frac{2\sqrt{2}}{3}$

Given,

${\int }_0^{\sqrt{2}}{x}^{2}dx$

$={\frac{x^{2+1}}{2+1}|}_0^{\sqrt{2}}$

$={\frac{x^3}{3}|}_0^{\sqrt{2}}$

$=\frac{2\sqrt{2}}{3}$