The value of the definite integral 8 3 8 11 + 4 cos 2 x + cos 4 x 1 - cos 4 x ?d x equals:

Question

The value of the definite integral $\int_{π / 8}^{3 π / 8} \frac{11 + 4 \cos 2 x + \cos 4 x}{1 - \cos 4 x} d x$ equals:

Smart Achievers · Accepted Answer

(4)

$2$ $| I |$ $= 2 \int_{π / 8}^{3 π / 8} \frac{1 + \cos 4 x}{1 - \cos 4 x} d x$

$\Rightarrow$ $| I |$ $= \int_{π / 8}^{3 π / 8} \frac{12 - (1 - \cos 4 x)}{1 - \cos 4 x} d x = 12 \int_{π / 8}^{3 π / 8} \frac{1}{2 \sin^{2} 2 x} d x - \int_{π / 8}^{3 π / 8} d x = 6 \int_{π / 8}^{3 π / 8} {cosec}^{2} 2 x d x - \frac{π}{4}$

$= {[- \frac{6}{2} \cot 2 x]}_{π / 8}^{3 π / 8} - \frac{π}{4} = - 3 [(1) + (1)] - \frac{π}{4} = - 6 - \frac{π}{4}$

Solution

Q.
The value of the definite integral $\int_{π / 8}^{3 π / 8} \frac{11 + 4 \cos 2 x + \cos 4 x}{1 - \cos 4 x} d x$ equals:

1 $- 6 + \frac{π}{4}$

2 $6 \sqrt{2} - \frac{π}{4}$

3 $12 - \frac{π}{2}$

4 $- 6 - \frac{π}{4}$

Want Us to Email you About Special Offers & Updates?

Solution

Q. The value of the definite integral ∫π/83π/811+4cos2x+cos4x1-cos4x dx equals:

1 -6+π4

2 62-π4

3 12-π2

4 -6-π4