Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y= 1/x^5, y = 0, x = 4, x = 6; about y = -3

We are tasked with finding the volume of the solid obtained by rotating the region bounded by the curves \( y = \frac{1}{x^5} \), \( y = 0 \), \( x = 4 \), and \( x = 6 \) about the axis \( y = -3 \).

This is a rotation around a horizontal axis below the region, so we will use the **method of cylindrical shells**. However, since the axis of rotation is not the x-axis, we'll adjust the formula for the radius of the shells.

### Step 1: Set up the Shell Method
For a solid formed by rotating a region around a line parallel to the x-axis, the volume is given by:

\[


Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = 1/x^5, y = 0, x = 4, x = 6; about y = -3

Learn how to find the volume of a solid obtained by rotating the region bounded by y = 1/x^5, y = 0, x = 4, and x = 6 about the line y = -3. This solution involves the cylindrical shell method, crucial calculus concepts, and step-by-step integration. Suitable for college-level calculus students.

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