# Volumes of Revolution

**Rotation About the x-axis**

Integration can be used to find the area of a region bounded by a curve whose equation you know. If we want to find the area under the curve y = x^{2} between x = 0 and x = 5, for example, we simply integrate x^{2} with limits 0 and 5.

Now imagine that a curve, for example y = x^{2}, is rotated around the x-axis so that a solid is formed. The volume of the shape that is formed can be found using the formula:

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**Rotation about the y-axis**

If the body is rotated about the y-axis rather than the x-axis, then we use the formula:

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