How to integrate sin²x?

Integration is an inverse process of differentiation. Let's use the concept of integration to solve the problem.

Answer: The integral of sin²x is x/2 - (sin2x)/4 + c .

Go through the explanation to understand better.

Explanation:

To solve:  ∫ sin²x

Let us first simplify sin²x, using the trigonometric identity

cos 2x = sin²x - cos²x

⇒ cos 2x = sin²x - (1 - sin²x)

⇒  cos 2x = 2sin²x - 1

⇒  (cos 2x + 1)/2 = sin²x

Now, using the simplified value for sin²x, the integral converts to:

 ∫ sin²x =  ∫ (cos 2x + 1)/2

 ∫ sin²x = x/2 - (sin2x)/4 + c   [Since the integral of cosax = - sinax / a]

where, c is the constant of integration

Thus, the integral of sin²x is x/2 - (sin2x)/4 + c .