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.
 Summer '10
 KUSHNER
 Multivariable Calculus

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