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Rotating a Curve About the X-axis

If a curve is rotated about the x-axis instead of the y-axis (Figure 6.4.14), we interchange x and y in the formulas for surface area,

06_applications_of_the_integral-225.gif (about x-axis),

06_applications_of_the_integral-226.gif (about x-axis),

06_applications_of_the_integral-227.gif (about x-axis).


Figure 6.4.14

Most of the time the formula for surface area will give an integral which cannot be evaluated exactly but can only be approximated, for example by the Trapezoidal Rule.

Last Update: 2006-11-05