Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Definite Integration

Question:

$\int\limits_{-π/2}^{π/2}\frac{e^{|\sin x|}.\cos x}{(1+e^{\tan x})}dx$ is equal to: 

Options:

e + 1

1 – e

e – 1

None of these

Correct Answer:

e – 1

Explanation:

$I=\int\limits_{0}^{π/2}(\frac{e^{\sin x}.\cos x}{1+e^{\tan x}}+\frac{e^{|\sin (-x)|}\cos x}{1+e^{\tan (-x)}})dx=\int\limits_{0}^{π/2}e^{\sin x}.\cos x\,dx=\int\limits_{0}^{1}e^t\,dt=e-1$