Thread: Double or Triple integration (Find the area ) Uncommon question

The question is:

Please click the picture above.
I let x^2+y^2=a^2 be the vertical cylinder, and I tried to find
1)the intersections between x^2+y^2=a^2 and z=2xy
2)the intersections between x^2+y^2=a^2 and z=x^2+y^2
and then don't know how to do.
I need to show the two area is the same, but i don't know how to show.

Hey happymatthematics.

What did you get for the intersections? (Once you have these then they become the limits for your area integral).

hello chiro,
the following is my attempt.


I found them in parametric form.
I now have three variables, including x, y, z, but I learnt to find area by double integration. so how to find area of three variables?

What are your limits of integration? You will be integrating over a region with specific limits.

Once you show the limits (and how you derived them), then we can take it from there.