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Mathematics · 2022 · 3 marks
CBSE 2022 · Region 3 · Set 1 · Q7
Evaluate: ∫_0^2 π (d x)/(1+ e^sin x)
Evaluate: $\displaystyle \int_{0}^{2 \pi} \frac{\mathrm{~d} x}{1+\mathrm{e}^{\sin x}}$
Marking-scheme solution
\[I=\int_{0}^{2 \pi} \frac{d x}{1+e^{\sin x}}
\]
\[I=\int_{0}^{2 \pi} \frac{d x}{1+e^{\sin (2 \pi-x)}}
\]
\[I=\int_{0}^{2 \pi} \frac{d x}{1+e^{-\sin x}}
\]
Adding ($\displaystyle 1$) and
\[2 I=\int_{0}^{2 \pi} 1 d x \Rightarrow 2 I=2 \pi
\]
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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.