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Set up an integral that represents the area of the surface obtained by rotating the given curve about the x-axis.

Set up an integral that represents the area of the surface obtained by rotating the given curve about the x-axis. Then use your calculator to ﬁnd the surface area correct to four decimal places.

asked Feb 2, 2015 in CALCULUS by anonymous
reshown Feb 2, 2015 by goushi

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1 Answer

Step 1:

The Parametric equations are and , .

Definition of the surface area:

If the curve given by the parametric equations and , is rotated about -axis, then the area of the resulting surface is given by

Consider .

Differentiate with respect to on each side.

Consider .

Differentiate with respect to on each side.

Step 2:

Substitute , and in surface area formula.

By using calculator,

Solution:

answered Feb 9, 2015 by Lucy Mentor

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