Question

Evaluate:
${\int }_0^1\frac{x^2+3x+2}{\sqrt{x}}dx$

• A. $\frac{42}{5}$
• B. $\frac{2}{5}$
• C. $\frac{32}{5}$
• D. None of these

Answer 1

The correct option is C $\frac{32}{5}$

${\int }_0^1\frac{x^2+3x+2}{\sqrt{x}}dx$

$={\int }_0^1\frac{x^2}{\sqrt{x}}+\frac{3x}{\sqrt{x}}+\frac{2}{\sqrt{x}}dx$

$={\int }_0^1(x^{3/2+3\sqrt{x}}+2x^{-1/2})dx$

$=\frac{x^{5/2}}{\frac{5}{2}}{\int }_0^1+\frac{3x^{3/2}}{3/2}{\int }_0^1+\frac{2x^{1/2}}{1/2}{\int }_0^1$

$=\frac{2}{5}+2+4$

$=6+\frac{2}{5}$

$=\frac{32}{5}$