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Problem1
| What is the surface area of the portion of the surface |
> z := x^2-y^2;
2 2
z := x - y
| that lies inside the cylinder, |
> x^2+y^2=9;
2 2
x + y = 9
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Solution:
| The element of surface area (sans dxdy) is given by, |
> dS := sqrt(1+diff(z,x)^2+diff(z,y)^2);
2 2 1/2
dS := (1 + 4 x + 4 y )
> Answer := Int(Int(dS,y=-sqrt(9-x^2)..sqrt(9-x^2)),x=-3..3) =
2 1/2
3 (9 - x )
/ /
| | 2 2 1/2
Answer := | | (1 + 4 x + 4 y ) dy dx = 117.3187007
| |
/ /
-3 2 1/2
- (9 - x )