#### Question Details

[answered] li (zl5676) - Homework 10 - woo - (53760) This print-out sh

I have attached my homework for my Multivariable Calculus course.

li (zl5676) ? Homework 10 ? woo ? (53760)

This print-out should have 10 questions.

Multiple-choice questions may continue on

the next column or page ? find all choices

before answering.

001 10.0 points By changing to polar coordinates evaluate

the integral

Z Z p

I =

x2 + y 2 dxdy 3. I = ?(1 ? e?3 )

4. I = ?(1 ? e?9 )

5. I = 1

?(1 ? e?9 )

4 6. I = 1

?(1 ? e?3 )

2 R when R is the region

n

o

2

2

(x, y) : 1 ? x + y ? 9, y ? 0 5. I = 32

?

3

38

?

3 0 17

3 3. I = 14

3 4. I = 16

3 5. I = 5 26

?

3

002 0 2. I = 6 29

2. I =

?

3 4. I = 10.0 points Evaluate the triple integral

Z 2Z yZ z

I =

(3z + y) dxdzdy .

1. I = 35

?

1. I =

3 3. I = 003 0 in the xy-plane. 1 004

10.0 points By changing to polar coordinates evaluate

the integral

Z Z

2

2

I =

e?x ?y dxdy

R when R is the region in the xy-plane bounded

by the graph of

p

9 ? y2

x =

and the y-axis.

1. I = 1

?(1 ? e?9 )

2 2. I = 1

?(1 ? e?3 )

4 10.0 points The solid E shown in li (zl5676) ? Homework 10 ? woo ? (53760)

is bounded by the graphs of

z = 1 ? x2 , 2 Use the transformation (x, y) ? (u, v) with x+y = 1, x = 4u , y = 2v and the coordinate planes x, y, z = 0. Write

the triple integral

Z Z Z

I =

f (x, y, z) dV to evaluate the integral

Z Z

I =

x2 dxdy as a repeated integral, integrating first with

respect to x, then z, and finally y. when R is the region bounded by the ellipse E Z 1 Z 1. 0 0 Z 1 Z y Z ? y 0 0 Z 1 Z 4. 1?z y ? ?1 3. ? Z 1 Z 0 Z Z 2. 0 0 0 1?z 0

1?z 0 ?

f (x, y, z) dx dz dy

f (x, y, z) dx dz dy

f (x, y, z) dx dz dy 1?z Z 1?y

0 005 R x2 y 2

+

= 1.

16

4

1. I = 32

2. I = 8?

3. I = 2

4. I = 8

f (x, y, z) dx dz dy 5. I = 2? 10.0 points Find the Jacobian of the transformation 6. I = 32? T : (u, v) ? (x(u, v), y(u, v))

when 2. 10.0 points Find the Jacobian of the transformation

x = 3u2 + v 2 , 1. 007 y = u2 + 3v 2 . ?(x, y)

= 26 uv

?(u, v) T : (r, ?) ? (x(r, ?), y(r, ?))

when

x = 4e?r cos ? , ?(x, y)

= 24 uv

?(u, v) y = 3er sin ? . ?(x, y)

3.

= 32 uv

?(u, v) 1. ?(x, y)

= ?12

?(r, ?) ?(x, y)

= 30 uv

?(u, v) 2. ?(x, y)

= 7e?2r

?(r, ?) ?(x, y)

= 28 uv

5.

?(u, v) 3. ?(x, y)

= 12 cos 2?

?(r, ?) 4. ?(x, y)

= ?7e?2r cos 2?

?(r, ?) 4. 006 10.0 points li (zl5676) ? Homework 10 ? woo ? (53760)

when R is the square having vertices ?(x, y)

5.

= 7e?2r cos 2?

?(r, ?)

6. (0, 0), (3, 4), (4, ?3), (7, 1). ?(x, y)

= ?12 cos 2?

?(r, ?)

008 3 1. I = 92 10.0 points Use polar coordinates to find the volume of

the solid shown in

z 2. I = 100

3. I = 75

4. I = 102 y 5. I = 25

010 x above the cone

z = p

x2 + y 2 and below the sphere x2 + y 2 + z 2 = 1 .

1. V

2. V

3. V

4. V

5. V

6. V ?

?

2? 2

=

3

2? ?

=

2

3

4? ?

=

2

3

??

=

2

3

?

4?

=

2? 2

3

?

2?

2? 2

=

3

009 10.0 points By using an appropriate linear transformation evaluate the integral

Z Z

I =

(x + y) dxdy

R 10.0 points Use an appropriate transformation to evaluate the integral

Z Z

I =

ex+y dxdy

D when D is the region

n

o

(x, y) : |x| + |y| ? 2

in the xy-plane shown in

2 y x

?2 2 ?2 1. I = 2e2

2. I = e2

3. I = e2 + e?2 li (zl5676) ? Homework 10 ? woo ? (53760)

4. I = 2 e2 ? e?2 5. I = e2 ? e?2

6. I = 2 e2 + e?2 4

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