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Rotating a curve to find the surface area

+2 votes

Find the area of the surface obtained my rotating the curve x=1+4y^2 about the x-axis from y = 1 to y = 2

asked Feb 26, 2013 in CALCULUS by johnkelly Apprentice

2 Answers

0 votes

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

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

Here is the answer for the curve rotating about the y - axis.

The rotating curve x = 1 + 4y2 about the y - axis from y = 1 to y = 2.

Differentiate the curve with respect to y.

dx/dy = 8y

⇒  dx/dy = 8y, a = 1, and b = 2.

image

image

image.

First find : image.

image

image

Apply formula : image.

image

image

image

image.

image.

answered Jul 30, 2014 by lilly Expert
0 votes

Contd...............

Then find  :  image.

Let,  image.

If, y = 1, then image.

If, y  = 2, then image

du = 128 dy

image

image

image

image

image

image

image

image

image

image

image.

image.

Substitute those values in equation (1).

image

image

image.

Therefore, the area of the surface obtained by rotating the curve x = 1 + 4y2 about the y - axis from y = 1 to y = 2 is 418.07π square units.

answered Jul 30, 2014 by lilly Expert

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