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Lecture 13-5 with diagram

Lecture 13-5 with diagram - course 4 Example 2 Set up an...

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Defn. Volume The volume of a closed, bounded region D in space is Note There are 6 ways to set up a triple integral. Tips on setting up bounds on triple integrals 1. 2. 2
Example 1 Let D be the solid bounded by the planes x = 0, x = 2, y = 0, z = 0 and y + z = 1. Find the volume of the solid by setting up all 6 orders of integration and evaluating one of them. 1. Integrate W.R.T. z first. Shadow in xy -plane 2. Integrate W.R.T. y first. Shadow in xz -plane 3. Integrate W.R.T. x first. Shadow in yz -plane 3

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Evaluate. All integrals will yield the same value (when set up properly, of

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Unformatted text preview: course) 4 Example 2 Set up an integral to nd the volume of the region formed by x = 4 y 2 + 4 z 2 and the plane x = 4. 5 Example 3 Find the volume of the region bounded by y + z = 1, y = x 2 and z = 0. 6 Example 4 Find the volume enclosed by z = 4-x 2-y 2 and z = x 2 + y 2 . 7 Example 5 Evaluate Z 2 Z 4-x 2 Z x sin 2 z 4-z dydzdx by changing the order of integration rst. 8...
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Lecture 13-5 with diagram - course 4 Example 2 Set up an...

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