Calculating Surface Area by Rotating a Curve - How to Find the Surface Area?

[Tranquility13]

Homework Statement

Find the area of the surface obtained by rotating the curve
y= 1+4 x^2
from x=0 to x = 8 about the y-axis.

Homework Equations

The Attempt at a Solution

 

[Yannick]

Hi

How did you try to solve it? Or don't you know how to start?

 

[Tranquility13]

Not sure how to start it.
Any assistance would be greatly appreciated.

 

[malawi_glenn]

Is this multidimensional calculus course?

If it is, how is surface interagrals defined?

(post in relevant HW-section in the future, this is not introductory physics)

 

[tiny-tim]

Find the area of the surface obtained by rotating the curve
y= 1+4 x^2
from x=0 to x = 8 about the y-axis.

Hi Tranquility13!

This is like the one about volumes.

again, divide it into horizontal slices at distance y above the x-axis, with height dy (so the slope is dy/dx).

what is the surface area of this slice (remember, it depends on the slope)?

get that, and then we'll do the integral.