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Find the area of the surface obtained by revolving the given curve about the indicated axis.?

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Find the area of the surface obtained by revolving the given curve about the indicated axis.?

y = 9 − x^2 on [0, 3]; y−axis
asked Feb 9, 2015 in CALCULUS by anonymous

1 Answer

0 votes

Step 1 :

The function is image and the interval is image.

For rotation about the y - axis, the surface area formula : image.

The function is image .

Solve for x .

image

The function is image .

Differentiate the curve with respect to y .

image

Evaluating boundaries :

If , then image.

If , then image.

Step 2 :

Substitute corresponding values in image.

The surface area is image.

image

Let image, then image.

Evaluating boundaries :

If image, then image.

If image, then image.

Substitute corresponding values in image.

image

The area of the surface by rotating the curve about the y - axis is 117.32 square units.

Solution :

The area of the surface by rotating the curve about the y - axis is 117.32 square units.

answered Feb 9, 2015 by lilly Expert

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