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
yx=
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.

External Links

Double Integral (Wolfram MathWorld)

Permanent Citation

Anton Antonov, Abby Brown
​
​"Double Integral for Volume"​
​http://demonstrations.wolfram.com/DoubleIntegralForVolume/​
​Wolfram Demonstrations Project​
​Published: April 29, 2007