https://file.aiquickdraw.com/mathbot/file/1726367616709x8acu461.jpg

The statement in the image is **True**.

Here's why:

The formula given describes the method of finding the volume of a solid of revolution. When rotating a region \( a \leq x \leq b \) about the x-axis, the volume of the resulting solid is calculated using:

\[
V = \int_a^b A(x) \, dx
\]

Where \( A(x) \) is the cross-sectional area of the solid at a particular \( x \)-coordinate.

1. **Disk Method:** 
   - If the cross-section is a disk, the area is \( A = \pi r^2 \), where \( r \) is the radius of the disk.
   
2. **Washer Method:** 
   - If the cross-section is a washer (a disk with a hole), the area is given by the difference between the area of the outer disk and the area of the inner disk: \( A = \pi R^2 - \pi r^2 \), where \( R \) is the outer radius and \( r \) is the inner radius.

Both of these descriptions align with the given information, making the statement **True**.

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Would you like further details or have any questions? 

Here are some related questions you might want to explore:
1. How do you apply the washer method when rotating around a different axis (e.g., the y-axis)?
2. Can the disk method be used for solids generated by rotating around axes other than the x-axis?
3. What is the difference between the shell method and the washer method for finding volumes?
4. How do you set up bounds of integration for irregular regions when using the disk or washer method?
5. What happens when the function to be rotated dips below the x-axis?

**Tip:** When solving problems involving the washer or disk method, always sketch the region being revolved to help set up the integral properly.

When we rotate a region (a ≤ x ≤ b) about the x-axis, volume of the resulting solid is V = ∫_a^b A(x) dx. If the cross section is a disk, then A = πr^2, where r is a variable that represents the radius of the disk. If the cross section is a washer, then A = πR^2 - πr^2, where R and r are variables. R represents the outer radius, and r represents the inner radius.

Understand how to find the volume of solids of revolution using the disk and washer methods. This problem involves the use of integral calculus to compute the volume by rotating a region around the x-axis. Suitable for students in Grades 11-12.

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