If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Surface integral ex3 part 1

Breaking apart a larger surface into its components. Created by Sal Khan.

Want to join the conversation?

• Why are we taking the integral of z?
• the question is just set up that way. We are taking the integral of z because it is the function in the given equation- if the z were zy^2 we would take the surface integral of zy^2.
• But the surface area of surface 1 is πr²=π, not 0, right?
• It gets multiplied by z, which is 0 for surface 1, so you end up with 0.
• Can we evaluate S2 by using a line integral concept since the surface is like an area of curtain between the x-y plane and z = 1 - x plane ?
• I was wondering how you would go about calculating the surface area of an intersection of two surfaces. Say you want to find the surface area of the surface cut out by x² + y² = 2x and x² + y² = z². You then know that z is the square root of 2x, but how do you find boundaries for x and y?
• What does taking a surface integral do? Does it give you the surface area?
(1 vote)
• It gives you the function for the surface area by throwing in a function in the formula.