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Double and Triple Integrals Using Iterated Integrals to find area Using Double Integrals to find Volume Using Triple Integrals to find Volume.

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Presentation on theme: "Double and Triple Integrals Using Iterated Integrals to find area Using Double Integrals to find Volume Using Triple Integrals to find Volume."— Presentation transcript:

1 Double and Triple Integrals Using Iterated Integrals to find area Using Double Integrals to find Volume Using Triple Integrals to find Volume

2 Three Dimensional Space

3 In Two-Dimensional Space, you have a circle In Three-Dimensional space, you have a _____________!!!!!!!!!!!

4 More 3-D graphs

5 The Iterated Integral

6 Setting up the Double Integral

7 Finding Area using Double Integrals

8 Compute the integral on the pictured region

9

10 Finding Volume using the Double Integral

11 Evaluate the volume using the region

12 Volume using the Triple Integral The cubes density is proportional to its distance away from the Xy-plane. Find its mass.

13


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