CBSE Class 12 Mathematics 2024: question 28(a)

Hints

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Step-by-step solution

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1. Let $I={\int }_0^{\pi }\frac{e^{\cos x}}{e^{\cos x}+e^{-\cos x}}dx$ …(i). Using ${\int }_0^{a}f(x)dx={\int }_0^{a}f(a-x)dx$ and $\cos (\pi -x)=-\cos x$: $I={\int }_0^{\pi }\frac{e^{-\cos x}}{e^{-\cos x}+e^{\cos x}}dx$ …(ii).

   1½ marks

2. Adding (i) and (ii): $2I={\int }_0^{\pi }1dx=[x{]}_0^{\pi }=\pi \Rightarrow I=\frac{\pi }{2}$.

   1½ marks

Answer: $\frac{\pi }{2}$

Revise the chapter

• Chapter: Integrals (notes, formulas, where marks are lost and every past question)
• Topic: Properties of Definite Integrals