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Double or Triple integration (Find the area ) Uncommon question

The question is:

Attachment 27369

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.

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

Hey happymatthematics.

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

1 Attachment(s)

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

hello chiro,

the following is my attempt.

Attachment 27378

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?

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

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.