Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Definite Integration

Question:

$\int\limits_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{d x}{1+\cos 2 x}$ is equal to

Options:

1

2

3

4

Correct Answer:

1

Explanation:

The correct answer is Option (1) - 1

$\int\limits_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{d x}{1+\cos 2 x}=\frac{1}{2}\int\limits_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\sec^2xdx$

$=\frac{1}{2}\left|\tan x\right|_{-\frac{\pi}{4}}^{\frac{\pi}{4}}=1$