CALC 2: Area of a Surface of Revolution: x=y+y^3 from 0 to 4

conniechung

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Hi, so I'm having trouble with one of my online calc homework..

Consider the following.
x=y+y^3 from 0 to 4

(a) Set up an integral for the area of the surface obtained by rotating the curve about the x-axis and the y-axis.
(i) the x-axis, the answer is S= 2piy(sqrt((3y^2+1)^2)+1)dy
(ii) the y-axis, the answer is S= 2pi(y^3+y)sqrt((3y^2+1)^2+1)dy

(b) Use the numerical integration capability of a calculator to evaluate the surface areas correct to four decimal places.
(i) the x-axis, the answer is 1258.6212
(ii) the y-axis, I'm really stuck on how to take the integral. I used wolfram to show how they did it, but I don't understand how they got it! I would really like to understand how to do this problem!

Thank you in advanced!
 
Hi, so I'm having trouble with one of my online calc homework..

Consider the following.
x=y+y^3 from 0 to 4

(a) Set up an integral for the area of the surface obtained by rotating the curve about the x-axis and the y-axis.
(i) the x-axis, the answer is S= 2piy(sqrt((3y^2+1)^2)+1)dy
(ii) the y-axis, the answer is S= 2pi(y^3+y)sqrt((3y^2+1)^2+1)dy

(b) Use the numerical integration capability of a calculator to evaluate the surface areas correct to four decimal places.
(i) the x-axis, the answer is 1258.6212
(ii) the y-axis, I'm really stuck on how to take the integral. I used wolfram to show how they did it, but I don't understand how they got it! I would really like to understand how to do this problem!

Thank you in advanced!
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