[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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