Calculating Area of Intersected Cylinders Using Line Integral

[khfrekek92]

Homework Statement

Two circular cylinders of radius a intersect so that their axes meet at right angles. Use a line integral to find the area of the part from one cut off by the other.

Homework Equations

line integral formula

The Attempt at a Solution

I'm lost as to where to set up the bounds and what to integrate.. thanks in advance for any help!

 

[Undoubtedly0]

Greetings! First parametrize one of the cylinders in cylindrical coordinates. Then try defining the bounds of integration using these coordinates (project the second cylinder down onto a circle).

 

[khfrekek92]

I got it! Thanks so much for your help! I wan't really understanding what line integrals were doing until now and it makes a lot more sense.. Thank you!