PLEASE SOLVE AND GIVE CORRECT ANSWER
Question 76 of 90
$\int_{0}^{π / 2} \frac{d x}{1 + \tan^{3} x}$ is :
1. 0
2. 1
3. $π$ /2
4. $π$ /4

Question

PLEASE SOLVE AND GIVE CORRECT ANSWER
Question 76 of 90
∫ 0 π / 2 d x 1 + tan 3 x is :
1 0
2 1
3 π /2
4 π /4

Varun Rawat · Accepted Answer

Let I = ∫0π/2dx1 + tan3x    ⇒I= ∫0π/2dx1 + sin3xcos3x⇒I = ∫0π/2cos3xcos3x + sin3x dx    
1⇒I = ∫0π/2cos3π2-xcos3π2 - x + sin3π2-xdx⇒I = ∫0π/2sin3xsin3x + cos3xdx     
2Adding 1 and 2, we get    2I = ∫0π/2sin3x + cos3xsin3x + cos3x dx⇒2I = ∫0π/2 dx⇒2I = x0π/2⇒2I = π2⇒I = π4

PLEASE SOLVE AND GIVE CORRECT ANSWER Question 76 of 90 ∫ 0 π / 2 d x 1 + tan 3 x is : 1. 0 2. 1 3. π /2 4. π /4

PLEASE SOLVE AND GIVE CORRECT ANSWER
Question 76 of 90
$\int_{0}^{π / 2} \frac{d x}{1 + \tan^{3} x}$ is :
1. 0
2. 1
3. $π$ /2
4. $π$ /4