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# Each integral represents the volume of a solid. Describe the solid.$2 \pi \displaystyle \int_{1}^4 \frac{y + 2}{y^2} dy$

## $x=\frac{1}{y^{2}}$ or $y=\frac{1}{\sqrt{x}}$

#### Topics

Applications of Integration

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##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

we know that D y implies the axis of rotation is horizontal. We know the rotation is about the X axis because the radius is why. Therefore, the height is why plus two over why Cubes. And we know that this represents the volume of the salt obtained by rotating the region bounded by axes. Why plus two over Why Cubed X zero wise one and wise for about the ex access Because again the radius would be in terms of why. Which means if we're drawing out a rough sketch of what this looks like, it would be approximate looking something like this, and I described the characteristics of the graph.

#### Topics

Applications of Integration

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp