How to integrate sin²x?

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

Answer: The integration of sin square x is x/2 - (sin 2x)/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 = ∫ 1 dx - (1/2) ∫ cos 2x dx

∫ sin²x = x/2 - (sin 2x)/4 + C [Since the integral of cos ax = sin ax / a]

☛Note: Here, ∫ cos 2x dx value can be computed using integration by substitution.

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

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