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The image shows the following integral problem:

\[
\int \sin^2(x) \, dx
\]

To solve this, we can use the trigonometric identity for \(\sin^2(x)\), which simplifies the integral:

\[
\sin^2(x) = \frac{1 - \cos(2x)}{2}
\]

Now substitute this into the integral:

\[
\int \sin^2(x) \, dx = \int \frac{1 - \cos(2x)}{2} \, dx
\]

This simplifies to:

\[
\frac{1}{2} \int (1 - \cos(2x)) \, dx
\]

We can now integrate each term:

\[
\frac{1}{2} \left( \int 1 \, dx - \int \cos(2x) \, dx \right)
\]

1. The integral of \(1\) with respect to \(x\) is \(x\).
2. The integral of \(\cos(2x)\) is \(\frac{\sin(2x)}{2}\) (using the chain rule).

Thus, we have:

\[
\frac{1}{2} \left( x - \frac{\sin(2x)}{2} \right) + C
\]

Simplifying the expression:

\[
\frac{x}{2} - \frac{\sin(2x)}{4} + C
\]

This is the final result.

Would you like more details or have any further questions?

Here are some related questions for further practice:
1. How do you integrate \(\int \sin^3(x) \, dx\)?
2. Can you solve \(\int \cos^2(x) \, dx\) using a similar method?
3. What is the general method for integrating trigonometric functions raised to powers?
4. How can you integrate products of sine and cosine functions?
5. How do you approach solving \(\int \sin^2(3x) \, dx\)?

**Tip:** Using trigonometric identities often simplifies integrals, making them easier to solve.

Find the integral of sin²(x) with respect to x.

Learn how to find the integral of sin²(x) using trigonometric identities. This problem involves key concepts in trigonometry and integration, suitable for students in Grades 11-12. Step-by-step solution and related practice problems included.

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