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Mathematics · 2026 · 3 marks
CBSE 2026 · Region 3 · Set 1 · Q27
Evaluate: ∫_0^π (sin^2026 x)/(sin^2026 x + cos^2026 x) d x
Evaluate : \[\int_{0}^{\pi} \frac{\sin ^{2026} \mathrm{x}}{\sin ^{2026} \mathrm{x}+\cos ^{2026} \mathrm{x}} d \mathrm{x} \]
Marking-scheme solution
Let $\displaystyle I=\int_{0}^{\pi} \dfrac{\sin^{2026} x}{\sin^{2026} x+\cos^{2026} x} dx=2 \int_{0}^{\frac{\pi}{2}} \dfrac{\sin^{2026} x}{\sin^{2026} x+\cos^{2026} x} dx$
Getting $\displaystyle I=2 \int_{0}^{\frac{\pi}{2}} \dfrac{\cos^{2026} x}{\sin^{2026} x+\cos^{2026} x} dx$
On adding, we get $\displaystyle 2 I=2 \int_{0}^{\frac{\pi}{2}} 1 dx \Rightarrow I=\dfrac{\pi}{2}$
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CBSE Class 12 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.