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Simpson's Rules for the area of a surface around the x-axis

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Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x-axis. Compare your answer with the value of the integral produced by your calculator. (Round your answer to six decimal places.)

y = sec x,
 
0 ≤ x ≤ π/6

 

asked Oct 27, 2016 in CALCULUS by anonymous
reshown Oct 27, 2016 by goushi

1 Answer

0 votes

Step 1:

The function is image and image.

Definition of surface area:

If the curve is described as  then the surface area of the curve obtained by rotating about the -axis is

The curve is image.

Differentiate on each side.

image
Area of the surface obtained by rotating the curve about the -axis is

image

Step 2:

Simpson's Rule:

Let image be continuous on image. The Midpoint Rule for approximating image is given by

,

where  and image

image

Using Simpson Rule, image

Step 3:

Area of the surface obtained by rotating the curve about the -axis is

image

Using calculator, the value of the integral is image

Solution:

Area of the surface obtained by rotating the curve about the -axis is image

answered Oct 27, 2016 by Anney Mentor

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