Homework 13

6 sin y 2 100 points 2 0 consequently calculate

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Unformatted text preview: case, Consequently, I= 010 I= 19 π. 6 −π sin π +y 2 10.0 points π /2 0 Consequently, Calculate the value of the double integral I= π + y + 2 cos(y ) 2 − 2 cos I=π . 2x sin(x + y ) dxdy A 011 when A is the rectangle (x, y ) : 0 ≤ x ≤ 1. I = (4 − π ) 2. I = 2π 3. I = −(4 − π ) 4. I = π correct π , 2 10.0 points Evaluate the integral 0≤y≤ π 2 . xexy dxdy I= A over the rectangle A = { (x, y ) : 0 ≤ x ≤ 3, 0 ≤ y ≤ 2 }. 1. I = 16 e −6 4 2. I = 16 e − 7 correct 2 . chester (crc2876) – HW13 – meth – (91845) 6 3. I = 16 e −6 2 2. I = 3 4. I = 16 e −5 4 3. I = 3 6 ln 6 − 5. I = 16 e −5 2 4. I = 3 19 36 ln 6 − 5 2 6. I = 16 e −7 4 5. I = 3 19 5 ln 6 − 36 4 Explanation: Since the integral with respect to y in A I= can be evaluated easily using substitution (or directly making the substitution in one’s head), while the integral with respect to x requires integration by parts, this suggests that we should represent the double integral as the repeated integral 3 2 I= 0 1 I= 10 0 0 e2x −x 2 3 0 , 6 6 (x...
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This note was uploaded on 08/25/2013 for the course MATH 408M taught by Professor Kushner during the Summer '10 term at University of Texas.

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