CALC HWK9 - Arwikar Dev – Homework 9 – Due 1:00 pm –...

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Unformatted text preview: Arwikar, Dev – Homework 9 – Due: Oct 30 2007, 1:00 pm – Inst: James Rath 1 This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. Number nine Number nine Number nine 001 (part 1 of 1) 10 points Evaluate the iterated integral I = Z 3 1 n Z 4 1 ( x + y ) 2 dx o dy . 1. I = ln 15 7 correct 2. I = 1 2 ln 15 7 3. I = 2 ln 15 7 4. I = 2 ln 3 2 5. I = 1 2 ln 3 2 6. I = ln 3 2 Explanation: Integrating the inner integral with respect to x keeping y fixed, we see that Z 4 1 ( x + y ) 2 dx = h- 1 x + y i 4 = n 1 y- 1 4 + y o . In this case I = Z 3 1 n 1 y- 1 4 + y o dy = h ln y- ln(4 + y ) i 3 1 . Consequently, I = ln ‡ (3)(1 + 4) (4 + 3) · = ln 15 7 . keywords: iterated integral, rational function, log integral 002 (part 1 of 1) 10 points Evaluate the iterated integral I = Z ln 6 ˆ Z ln 5 e 2 x- y dx ! dy . 1. I = 11 2. I = 8 3. I = 9 4. I = 10 correct 5. I = 7 Explanation: Integrating with respect to x with y fixed, we see that Z ln 5 e 2 x- y dx = 1 2 h e 2 x- y i ln 5 = 1 2 ‡ e 2 ln 5- y- e- y · = ‡ 5 2- 1 2 · e- y . Thus I = 12 Z ln 6 e- y dy =- 12 h e- y i ln 6 =- 12 ‡ e- ln 6- 1 · . Consequently, I =- 12 ‡ 1 6- 1 · = 10 . keywords: Arwikar, Dev – Homework 9 – Due: Oct 30 2007, 1:00 pm – Inst: James Rath 2 003 (part 1 of 1) 10 points Determine the value of the double integral I = Z Z A 3 xy 2 4 + x 2 dA over the rectangle A = n ( x, y ) : 0 ≤ x ≤ 3 ,- 4 ≤ y ≤ 4 o , integrating first with respect to y . 1. I = 64 ln ‡ 4 13 · 2. I = 64 ln ‡ 13 4 · correct 3. I = 64 ln ‡ 13 8 · 4. I = 32 ln ‡ 13 8 · 5. I = 32 ln ‡ 4 13 · 6. I = 32 ln ‡ 13 4 · Explanation: The double integral over the rectangle A can be represented as the iterated integral I = Z 3 µZ 4- 4 3 xy 2 4 + x 2 dy ¶ dx , integrating first with respect to y . Now after integration with respect to y with x fixed, we see that Z 4- 4 3 xy 2 4 + x 2 dy = h xy 3 4 + x 2 i 4- 4 = 128 x 4 + x 2 . But Z 3 128 x 4 + x 2 dx = h 64 ln(4 + x 2 ) i 3 . Consequently, I = 64 ln ‡ 13 4 · . keywords: 004 (part 1 of 1) 10 points Evaluate the integral, I , of the function f ( x, y ) = 3 xe 2 xy over the rectangle A = { ( x, y ) : 0 ≤ x ≤ 2 , ≤ y ≤ 2 } . 1. I = 3 16 ‡ e 8- 8 · 2. I = 3 8 ‡ e 8- 8 · 3. I = 3 8 ‡ e 8- 7 · 4. I = 3 16 ‡ e 8- 7 · 5. I = 3 8 ‡ e 8- 9 · correct 6. I = 3 16 ‡ e 8- 9 · Explanation: The integral is given by I = Z Z A 3 xe 2 xy dxdy....
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This note was uploaded on 02/25/2010 for the course M 54363 taught by Professor Olsen during the Fall '07 term at University of Texas.

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CALC HWK9 - Arwikar Dev – Homework 9 – Due 1:00 pm –...

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