# Computing surface area with double integrals help

• Apr 29th 2009, 09:20 PM
qtpipi
Computing surface area with double integrals help
Compute the surface area of the part of the cylinder x^2 + y^2 = 1, z>=0, between the planes y=0 and z=y+1

And one more!: Find the area of the triangle with vertices (1,2,0), (3,0,7), and (-1,0,0) using a surface integral. Check your answer using the cross product

I have no idea how to do these.
• Apr 30th 2009, 01:34 AM
Calculus26
In the first case make sure you are familiar with the surface area formula for a function z = f(x,y)

In your first problem use the analagous formula where x = f(y,z)

In particular:

x= (1-y^2)^(1/2)

dS = [(dx/dy)^2 + (dx/dz)^2 +1]^(1/2) dzdy

By Symmetry you can do half and double it

The region of integration is the trapezoidal region in the yz plane

where z varies from 0 to y + 1 and y varies from 0 to 1.

In the second problem you should know how to find the equation of a plane using 3 points. You probably did this much earlier in the semester so if you forgot look it up.

Once you have z = f(x,y) then it is fairly easy to see the region of integration in the xy plane is the triangular region with vertices

(-1,0), (1,2), and (3,0)