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Mathematics · 2022 · 3 marks
CBSE 2022 · Region 5 · Set 3 · Q9
Evaluate: ∫_1^3 (√ x)/(√ x +√(4- x)) dx
Evaluate : $\displaystyle \int_{1}^{3} \frac{\sqrt{\mathrm{x}}}{\sqrt{\mathrm{x}}+\sqrt{4-\mathrm{x}}} \mathrm{dx}$
Marking-scheme solution
\[\begin{aligned}
I & =\int_{1}^{3} \frac{\sqrt{x}}{\sqrt{x}+\sqrt{4-x}} d x \\
& =\int_{1}^{3} \frac{\sqrt{4-x}}{\sqrt{4-x}+\sqrt{x}} d x \quad \text { (using property) } \\
& \left.\Rightarrow 2 I=\int_{1}^{3} 1 d x=x\right]_{1}^{3}=2 \\
& \Rightarrow I=1
\end{aligned}
\]
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CBSE Class 12 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.