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

More 3-D graphs

The Iterated Integral

Setting up the Double Integral

Finding Area using Double Integrals

Compute the integral on the pictured region

Finding Volume using the Double Integral

Evaluate the volume using the region

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