Problem

$\int \sin ^{2} x d x$

Solution

Step 1 :Given the integral of \(\sin^2 x\)

Step 2 :We can solve this using the power-reduction identity. The power-reduction identity for \(\sin^2 x\) is \(\sin^2 x = \frac{1 - \cos(2x)}{2}\)

Step 3 :Substitute this into the integral and then solve

Step 4 :\(x = x\)

Step 5 :Integral = \(\frac{x}{2} - \frac{\sin(2x)}{4}\)

Step 6 :The integral of \(\sin^2 x\) is \(\frac{x}{2} - \frac{\sin(2x)}{4}\)

Step 7 :Final Answer: \(\boxed{\frac{x}{2} - \frac{\sin(2x)}{4}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/7277/

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