How to integrate sin^2x?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The inverse process of differentiation is integration.

Let us integrate sin²x

∫ sin²x

Using the trigonometric identity, let us simplify sin²x

cos 2x = sin²x – cos²x

Table of content

We can write it as

cos 2x = sin²x – (1 – sin²x)

So we get

cos 2x = 2sin²x – 1

(cos 2x + 1)/2 = sin²x

By using the simplified value of sin²x

∫ sin²x = ∫ (cos 2x + 1)/2

∫ sin²x = x/2 – (sin2x)/4 + c

As cosax = – sinax / a

Where c is the constant of integration

So if asked, How to integrate sin²x? then the answer will be that the integral of sin²x is x/2 – (sin2x)/4 + c.

Summary:

How to integrate sin²x?

The integral of sin²x is x/2 – (sin2x)/4 + c.

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