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The image contains several mathematical problems related to calculus and algebra. Here are the questions extracted from the image:

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**Unit IV**

1. **Find the value of \(\int \sin^2 x \, dx\)**

2. **Integrate the following function with respect to \(x\):**

   \[
   \int x \sqrt{2x + 3} \, dx
   \]

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3. **Evaluate \(\int x^2 e^x \, dx\)**

4. **Integrate the following function with respect to \(x\):**

   \[
   \int \frac{x^3}{\sqrt{1 - x^2}} \, dx
   \]

5. **Find the area bounded by the curves \(y = 2x - x^2\) and \(y = x\) with the x-axis.**

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Explore calculus problems involving integration and finding the area under curves. This page includes step-by-step solutions to problems such as evaluating integrals and finding bounded areas between curves. Suitable for advanced high school students.

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