How to integrate sin^2x?

By Shivank Goel|Updated : August 1st, 2022

The inverse process of differentiation is integration.

Let us integrate sin2x

∫ sin2x

Using the trigonometric identity, let us simplify sin2x

cos 2x = sin2x - cos2x

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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