Question

The value of $\underset{2}{\overset{8}{\int }}\frac{\sqrt{10-x}}{\sqrt{x}+\sqrt{10-x}}dx$ is

• A. $10$
• B. $0$
• C. $8$
• D. $3$

Answer 1

The correct option is D $3$

$\text{Let I}=\underset{2}{\overset{8}{\int }}\frac{\sqrt{10-x}}{\sqrt{x}+\sqrt{10-x}}dx\cdots \left(1\right)$
$\text{Then, I}=\underset{2}{\overset{8}{\int }}\frac{\sqrt{10-(2+8-x)}}{\sqrt{2+8-x}+\sqrt{10-(2+8-x)}}dx$
$\Rightarrow I=\underset{2}{\overset{8}{\int }}\frac{\sqrt{x}}{\sqrt{10-x}+\sqrt{x}}dx\cdots \left(2\right)$
Adding $\left(1\right)$ and $\left(2\right)$, we get
$2I=\underset{2}{\overset{8}{\int }}dx$
$\Rightarrow I=3$