HW_10 - Assignment Previewer Page 1 of 15 HW 10 (1299041)...

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HW 10 (1299041) Current Score: 0/53 Due: Mon Jun 28 2010 11:59 PM CDT Question Points Total 0/53 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0/3 0/2 0/4 0/2 0/2 0/2 0/2 0/2 0/2 0/2 0/2 0/2 0/2 0/2 0/2 0/2 0/2 0/2 0/2 0/2 0/2 0/2 0/2 0/2 0/2 Description 16.1, Double integrals over rectangles; 16.2, Iterated integrals; 16.3, Double integrals over general regions. SCalc6 16.1.001.MI. [1386582] 1. 0/3 points (a) Estimate the volume of the solid that lies below the surface z = xy and above the following rectangle. R = ( x , y )| 2 x 8 , 2 y 6 Use a Riemann sum with m = 3, n = 2, and take the sample point to be the upper right corner of each square. V = Enter an exact number. 720 Page 1 of 15 Assignment Previewer 6/21/2010 ..
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(b) Use the Midpoint Rule to estimate the volume of the solid in part (a). V = Enter an exact number. 480 Solution or Explanation (a.) The subrectangles are shown in the figure. The surface is the graph of f ( x , y ) = xy and Δ A = 4, so we estimate V Δ A = f ( 4 , 4 ) Δ A + f ( 4 , 6 ) Δ A + f ( 6 , 4 ) Δ A + f ( 6 , 6 ) Δ A + f ( 8 , 4 ) Δ A + f ( 8 , 6 ) Δ A 3 i =1 2 f ( x i , y i ) j =1 = 16 ( 4 ) + 24 ( 4 ) + 24 ( 4 ) + 36 ( 4 ) + 32 ( 4 ) + 48 ( 4 ) = 720 Assume: a = 6 b = 4 c = 4 d = 6 Page 2 of 15 Assignment Previewer 6/21/2010 ..
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(b.) e = 8 V Δ A = f ( 3 , 3 ) Δ A + f ( 3 , 5 ) Δ A + f ( 5 , 3 ) Δ A + f ( 5 , 5 ) Δ A + f ( 7 , 3 ) Δ A + f ( 7 , 5 ) Δ A 3 i =1 2 f ( x i , y i ) j =1 = 9 ( 4 ) + 15 ( 4 ) + 15 ( 4 ) + 25 ( 4 ) + 21 ( 4 ) + 35 ( 4 ) = 480 SCalc6 16.1.002. [832776] 2. 0/2 points If R = [ -1 , 3 ][ 4 , 6 ], use a Riemann sum with m = 4, n = 2 to estimate the value of the following. Page 3 of 15 Assignment Previewer 6/21/2010 ..
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Take the sample points to be the upper left corners of the squares. The value of integral is
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This note was uploaded on 04/10/2012 for the course MATH 251 taught by Professor Mccray during the Summer '10 term at Illinois Tech.

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HW_10 - Assignment Previewer Page 1 of 15 HW 10 (1299041)...

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