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 = cos²x - sin²x

⇒ cos 2x = (1 - sin²x) - sin²x

⇒  cos 2x = 1 - 2sin²x

⇒  (1 - cos 2x)/2 = sin²x

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

 ∫ sin²x dx =  ∫ (1 - cos 2x)/2 dx

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

where, c is the constant of integration. For more information, click here.

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