Learn How To Integrate Sin²(X) Using Trigonometric Identity | Step-By-Step Guide

∫sin²(x)dx

(1/2)x-(1/2)sin(x)cos(x)+C

To integrate ∫sin²(x)dx, we can use the trigonometric identity:

sin²(x) = (1/2)(1-cos(2x))

Therefore, we can write:

∫sin²(x)dx = ∫(1/2)(1-cos(2x))dx

Using the linearity of integration, we can split it up as:

(1/2)∫dx – (1/2)∫cos(2x)dx

The first term integrates to:

(1/2)∫dx = (1/2)x + C

The second term involves a trigonometric function, which we can integrate as follows:

∫cos(2x)dx = (1/2)sin(2x) + C

Putting everything together, we get:

∫sin²(x)dx = (1/2)x – (1/4)sin(2x) + C

where C is the constant of integration. Therefore, this is the final answer.

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