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Mathematics · 2025 · 2 marks
CBSE 2025 · Region 2 · Set 1 · Q22
Evaluate: ∫_0^((π)/4) √(1+ sin 2 x) d x
Evaluate: $\displaystyle \int_{0}^{\frac{\pi}{4}} \sqrt{1+\sin 2 x} \mathrm{~d} x$
Marking-scheme solution
Given definite integral $\displaystyle =\int_{0}^{\frac{\pi}{4}} \sqrt{(\sin x+\cos x)^{2}} d x$
\[=\int_{0}^{\frac{\pi}{4}}(\sin x+\cos x) d x
\]
$\displaystyle =1$
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CBSE Class 12 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.