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Integrals

Question

Evaluate: $\int_{0}^{π} \frac{e^{cosx}}{e^{cosx} + e^{- cosx}}$

Solution

$Let I = \int_{0}^{π} \frac{e^{cosx}}{e^{cosx} + e^{- cosx}} dx Using \int_{0}^{a} f (x) = \int_{0}^{a} f (a - x) dx I = \int_{0}^{π} \frac{e^{\cos (π - x)}}{e^{\cos (π - x)} + e^{- \cos (π - x)}} . dx 2 I = \int_{0}^{π} \frac{e^{- \cos x} + e^{\cos x}}{e^{\cos x} + e^{- \cos x}} . dx I = \frac{1}{2} \int_{0}^{π} dx = \frac{1}{2} [π - 0] I = \frac{π}{2}$

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Integrals

Evaluate: $\int_{0}^{π} \frac{e^{cosx}}{e^{cosx} + e^{- cosx}}$

Some More Questions From Integrals Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Integrals

Evaluate: ∫0π ecosxecosx + e-cosx

Some More Questions From Integrals Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Evaluate: $\int_{0}^{π} \frac{e^{cosx}}{e^{cosx} + e^{- cosx}}$