double and triple integrals using iterated integrals to find area using double integrals to find...
TRANSCRIPT
Double and Triple Integrals
•Using Iterated Integrals to find area•Using Double Integrals to find Volume•Using Triple Integrals to find Volume
Three Dimensional Space
In Two-Dimensional Space, you have a circleIn Three-Dimensional space, you have a _____________!!!!!!!!!!!
More 3-D graphs
The Iterated Integral2
1
2y
xydx2
2 2
1 1
2 2x
x y ydydx
Setting up the Double Integral
Finding Area using Double Integrals
Compute the integral on the pictured region
2
R
xy dA
Compute the integral on the pictured region
2
R
xy dA
Finding Volume using the Double Integral
Evaluate the volume using the region
2 21 11
2 2R
x y dA 0 1x 0 1y
Volume using the Triple Integral4 4 4
0 0 0
dV
The cubes density is proportional to its distance away from theXy-plane. Find its mass.
12
0 0 0
x yx
dV