lecture 22-23 CH 15.1. Double Integrals

# lecture 22-23 CH 15.1. Double Integrals - CH. 15.1 Double...

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Math 234 SS 2008 CH. 15.1 Double Integrals. Lectures #22-23 Definition of Double Integrals for Rectangular Planar Region. ( 29 , z f x y = is defined on : , R a x b c y d f 1

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Math 234 SS 2008 CH. 15.1 Double Integrals. Lectures #22-23 Definition. ( 29 ( 29 0 1 lim , , k k k P k R f x y A f x y dA f f = = Equivalent writing: ( 29 , R f x y dxdy . Double Integrals as Volumes. When ( 29 , f x y is a positive function over a rectangular region R in xy -plane, the double integral of f over R may be interpreted as the volume. 2
Math 234 SS 2008 CH. 15.1 Double Integrals. Lectures #22-23 Fubini’s Theorem for Calculating Double Integrals. Example. Calculate ( 29 4 R x y dydx - - over the rectangular region 3

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Math 234 SS 2008 CH. 15.1 Double Integrals. Lectures #22-23 : 0 2, 0 1 R x y f This integral may be interpreted as the volume under the plane 4 z x y = - - over the rectangular region R. 4
Math 234 SS 2008 CH. 15.1 Double Integrals. Lectures #22-23 Problems . Evaluate the following integrals. 1. 7 2 4 1 2 y dxdy - - 5

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Math 234 SS 2008

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Unformatted text preview: CH. 15.1 Double Integrals. Lectures #22-23 2. ( 29 10 2 x y dxdy + 3. ( 29 10 13 sin cos x y dxdy π + Double Integrals over Bounded Nonrectangular Regions. 6 Math 234 SS 2008 CH. 15.1 Double Integrals. Lectures #22-23 7 Math 234 SS 2008 CH. 15.1 Double Integrals. Lectures #22-23 Problems . 4. Find the volume of the region below 2 z x y = and over the region 8 : 0, 1 , 1 R x x y x y = = = = Math 234 SS 2008 CH. 15.1 Double Integrals. Lectures #22-23 Finding the Limits of Integration. 9 Math 234 SS 2008 CH. 15.1 Double Integrals. Lectures #22-23 10 Math 234 SS 2008 CH. 15.1 Double Integrals. Lectures #22-23 Problems . 5. Reverse the order of integration of the integral 64 8 y y dxdy . 6. Find the area of the plane region bounded by curves 2 y x and y x = = . 11 Math 234 SS 2008 CH. 15.1 Double Integrals. Lectures #22-23 12...
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## This note was uploaded on 03/19/2008 for the course MATH 234 taught by Professor Kadyrova during the Spring '08 term at Michigan State University.

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lecture 22-23 CH 15.1. Double Integrals - CH. 15.1 Double...

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