Question

Evaluate the integral
${\int }_2^3\frac{\sqrt{x}}{\sqrt{5-x}+\sqrt{x}}dx$

• A. $1/2$
• B. $3/2$
• C. $5/2$
• D. $0$

Answer 1

The correct option is A $1/2$

$I={\int }_3^2\frac{\sqrt{x}}{\sqrt{5-x}+\sqrt{x}}dx$

${\int }_a^{b}f\left(x\right)dx={\int }_a^{b}f\left[\right(a+b)-x]dx$

$I={\int }_2^3\frac{\sqrt{5-x}}{\sqrt{x}+\sqrt{5-x}}dx$

$2I={\int }_2^{3}1\cdot dx$

Thus $2I=1$

$I=\frac{1}{2}$