https://file.aiquickdraw.com/mathbot/file/1725841943760c2e44m4j.jpg

The image contains a mathematical problem that involves evaluating an integral to find the volume of a solid of revolution. Here's a step-by-step breakdown of the problem and the solution process:

### Problem Summary:
The task involves evaluating an integral to determine the volume of a solid formed by rotating a region around the y-axis.

### Mathematical Expression:
The volume of the solid of revolution is given by:
\[
V = 2\pi \int_a^b x f(x) \, dx
\]

The image specifies the function \( f(x) \), the bounds, and the graph of the region being rotated.

### Graph Analysis:
The graph shows a shaded area that is being rotated around the y-axis, with bounds given for integration.

### Solution Steps:
1. **Identify the function \( f(x) \) and the interval \( [a, b] \)**:
   - Function: \( f(x) \) (not fully readable from the image, assumed contextually)
   - Bounds: \( a \) to

Evaluate the integral to find the volume of the solid formed by rotating a region around the y-axis.

Learn how to calculate the volume of a solid of revolution by evaluating an integral. The problem involves rotating a region around the y-axis using the disk method. Suitable for students in Grades 11-12.

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