Trigonometric Integration by Substitution

Trigonometric Integration by Substitution

Trigonometric Integration by Substitution can be handled using the basic rules such as \( \displaystyle \frac{d}{dx} \sin{x} = \cos{x} \text{ and } \frac{d}{dx} \cos{x} = -\sin{x} \).

Practice Questions of Trigonometric Integration by Substitution

Question 1

Find \( \displaystyle \int{\sin{x}\cos^2{x}}dx \).

Question 2

Find \( \displaystyle \int{\cos{x}\sin^2{x}}dx \).

Question 3

Find \( \displaystyle \int{\sin^3{x}}dx \).

Question 4

Find \( \displaystyle \int{\sin^5{x}}dx \).

Question 5

Find \( \displaystyle \int{\cos^3{x}}dx \).

Question 6

Find \( \displaystyle \int{\cos^5{x}}dx \).

Question 7

Find \( \displaystyle \int{\sin^3{x}\cos^3{x}}dx \).

Question 8

Find \( \displaystyle \int{\sin^5{x}\cos^4{x}}dx \).

Question 9

Find \( \displaystyle \int{\sec^4{x}}dx \).

Question 10

Find \( \displaystyle \int{\sec^6{x}}dx \).