MCQ
$\int_a^b \frac{\sqrt{x}}{\sqrt{x}+\sqrt{a+b-x}} d x=$
- A$a+b$
- B$\frac{b-a}{2}$
- C$a-b$
- D$\frac{a-b}{2}$
$
\begin{aligned}
& \text {(b) : Let } I=\int_a^b \frac{\sqrt{x}}{\sqrt{x}+\sqrt{a+b-x}} d x ...(i) \\
& \Rightarrow I=\int_a^b \frac{\sqrt{a+b-x}}{\sqrt{a+b-x}+\sqrt{x}} d x ..(ii) \\
& {\left[\because \int_a^b f(x) d x=\int_a^b f(a+b-x) d x\right]}
\end{aligned}
$
Adding (i) and (ii), we get
$
\begin{aligned}
& 2 I=\int_a^b \frac{\sqrt{x}+\sqrt{a+b-x}}{\sqrt{x}+\sqrt{a+b-x}} d x=\int_a^b d x=[x]_a^b=b-a \\
& \Rightarrow I=\frac{b-a}{2}
\end{aligned}
$
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| $X:$ | $0$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ |
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