Math3CHomework#7
Dueat3:30PMonThursday,April6th2017
Good luck!
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Evaluate the integral.
3
y
1)
x2y 2 dx dy
1
0
364
A)
9
∫
2)
3
ln x
∫ ∫
1
3)
∫
∫
364
3
C)
∫
350
3
D)
350
9
2)
B) 2
ln 10
10
C) 1
D) 8
e y dx dy
3)
ey
A)
∫
B)
e y dy dx
0
A) 4
0
4)
1)
81
4
!/10
0
B)
∫
cos 5x
121
4
C)
121
2
D)
81
2
sin 5x dy dx
4)
0
A)
1
20
B)
1
10
C)
!
10
Integrate the function f over the given region.
5) f(x, y) = xy over the triangular region with vertices (0, 0), (10, 0), and (0, 6)
5
A)
B) 25
C) 15
2
D)
!
20
5)
D) 150
6) f(x, y) = x + y over the trapezoidal region bounded by the x-axis, y-axis, line x = 6, and line
6 2
y =-
6)
1
x+4
3
A) 18
B) 30
C) 46
D) 22
7) f(x, y) = 1 over the region bounded by the x-axis, line x = 9, and curve y = ln x
ln x
A) 8
B) 10
C) 9
1
D) 1
7)
Reverse the order of integration and then evaluate the integral.
12
4
cos x dx dy
8)
x
0
y/3
A) 3 sin 4
B) 4 cos 3
C) 3 cos 4
∫
9)
∫
∫
4
ln 8
ln 8
∫
0
∫
9)
y/4
14
B) 14
7
∫
0
C) 20
10)
y/2
B)
C)
49
1
tan-1 49 - ln 2402
2
2
1
4
∫ ∫
0
D) 12
tan-1 x2 dx dy
A) 49 tan-1 49 - 1 ln 2402
11)
D) 4 sin 3
2
e x dx dy
A) 18
10)
8)
49
tan-1 49 - 1 ln 2402
2
1
D) 49 tan-1 49 - ln 2402
2
2
x4 e x y dx dy
11)
4y
A) e 16 - 1
B)
4e 16 - 68
3
C) 4e 16 - 68
D) e 16 - 68
3
Use the given transformation to evaluate the integral.
12) u = x + y, v = -2x + y;
∫∫
12)
-2x dx dy,
R
where R is the parallelogram bounded by the lines y = -x + 1, y = -x + 4, y = 2x + 2, y = 2x + 5
A) 4
B) -2
C) -4
D) 2
13) u = x + y, v = -2x + y;
∫∫
13)
(-5x + 3y) dx dy,
R
where R is the parallelogram bounded by the lines y = -x + 1, y = -x + 4, y = 2x + 2, y = 2x + 5
49
49
61
61
A)
B)
C)
D)
4
2
2
4
14) u = -6x + y, v = 10x + y;
∫∫
14)
(y - 6x) dx dy,
R
where R is the parallelogram bounded by the lines y = 6x + 3, y = 6x + 5, y = -10x + 6,
y = -10x + 8
A) 2
B) 1
C) 256
D) 512
2
15) u = -8x + y, v = 5x + y;
∫∫
15)
(5x + y) dx dy,
R
where R is the parallelogram bounded by the lines y = 8x + 3, y = 8x + 6, y = -5x + 5,
y = -5x + 10
2925
225
225
A)
B)
C)
D) 2925
2
26
13
Change the Cartesian integral to an equivalent polar integral, and then evaluate.
0
4
x2 + y 2 dx dy
16)
-4 - 16 - y 2 1 + x2 + y 2
∫ ∫
A)
17)
4
∫ ∫
!(8 + ln 5)
4
16 - x2
-4
- 16 - x2
16
A)
!
17
B)
!(8 + 2 ln 5)
2
C)
!(8 + 2 ln 5)
4
16)
D)
!(8 + ln5)
2
1
dy dx
(1 + x2 + y 2) 2
B)
17)
16
!
33
C)
64
!
17
D)
32
!
17
Find the Jacobian for the given transformation.
18) x = 6u2, y = 2uv
A) 12u2
18)
B) 24u2
C) 12v 2
19) x = 5u cosh 6v, y = 5u sinh 6v
A) 180v
B) 180u
D) 24v 2
19)
C) 150v
3
D) 150u