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Mathematics · 2023 · 3 marks
CBSE 2023 · Region 3 · Set 1 · Q27
Evaluate: ∫_1^3 (√(4- x))/(√ x +√(4- x)) d x
Evaluate : \[\int_{1}^{3} \frac{\sqrt{4-\mathrm{x}}}{\sqrt{\mathrm{x}}+\sqrt{4-\mathrm{x}}} d \mathrm{x} \]
Marking-scheme solution
Let $\displaystyle \mathrm{I}=\int_{1}^{3} \frac{\sqrt{4-\mathrm{x}}}{\sqrt{\mathrm{x}}+\sqrt{4-\mathrm{x}}} \mathrm{dx}$
$$\mathrm{I}=\int_{1}^{3} \frac{\sqrt{4-(4-\mathrm{x})}}{\sqrt{4-\mathrm{x}}+\sqrt{4-(4-\mathrm{x})}} \mathrm{dx}
$$
$$2 \mathrm{I}=\left.\mathrm{x}\right|_{1} ^{3}=2
$$
$$\Rightarrow \mathrm{I}=1
$$
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CBSE Class 12 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.