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WOLFRAM|DEMONSTRATIONS PROJECT

Double Integral for Volume

​
circular paraboloid
hyperbolic paraboloid
prisms
9
f(x,y)=
-
2
x
-
2
y
+9
2
x
+
2
y
≤9
0
2
x
+
2
y
>9
n=9 Δx=2. Δy=2.
volume=132.
3
∫
-3
3
∫
-3
9-
2
x
-2
2
y
2
x
+
2
y
≤9
0
2
x
+
2
y
>9
yx=
81π
2
show surface
Increase the number of rectangular prisms to generate volume approximations closer to the true value. Note that some prisms effectively have zero volume.
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