How to integrate sin squared?

We will use the concept of cos double angle formula for Integration of sin square.

Answer: The final integral of sin²x is (1/2)x - (1/4)sin(2x) + C

Let's understand how we arrived at the solution.

Explanation:

Given: sin²(x)

cos(2x) = 1 - 2sin²(x)  [From cos double angle Trigonometric identities]

sin²(x) = (1/2)(1 - cos(2x)

Integrate on both the sides

∫sin²(x)dx = ∫(1/2)(1 - cos(2x) dx

=(1/2) × ∫(1 - cos(2x)) dx 

= 1/2 × (x - 1/2sin(2x)) + C

Thus, ∫sin²(x) dx = (1/2)x - (1/4)sin(2x) + C

Hence,the final integral of  sin²x is (1/2)x - (1/4)sin(2x) + C