Chapter 14.3 Practice Problems - math.drexel.edu
Chapter 14.3 Practice Problems
EXPECTED SKILLS:
? Be able to convert rectangular double integrals to polar double integrals, including converting the limits of integration, the function to be integrated, and the differential dA to r dr d.
PRACTICE PROBLEMS:
1. Consider the region R shown below which is enclosed by x2 + y2 = 1, x2 + y2 = 4, y = x and the x axis.
Fill in the missing limits of integration: f (x, y) dA =
R
2
f (x, y) dA =
f (r, )r dr d
/4 1 R
f (r, )r dr d.
For problems 2-6, evaluate the iterated integral by converting to polar coordinates.
4
16-x2
2.
00
x2 + y2 dy dx
32
3
3/ 2
9-x2
3.
x2 + y2 2 dy dx
0
x
243
8
1
2
2x-x2
4.
xy dy dx
00
2
3
5. Evaluate (x - y) dA where R = {(x, y) : 4 x2 + y2 16 and y x}
R
112 2
3
6. Evaluate
e-(x2+y2)
dA
where
R
=
{(x,
y)
:
x2
+
y2
3
and
0
y
3x}
R
1
1-
6
e3
7. Use a double integral in polar coordinates to calculate the area of the region which is inside of the cardioid r = 2 + 2 cos and outside of the circle r = 3. 93 - 2
8. Use a double integral in polar coordinates to calculate the area of the region which is common to both circles r = 3 sin and r = 3 cos . 5 3 3 - 84
9. Consider the top which is bounded above by z = 4 - x2 - y2 and bounded below by z = x2 + y2, as shown below.
2
Use a double integral in polar coordinates to calculate the volume of the top.
16 8 2
-
3
3
10. Consider the surfaces x2 + y2 + z2 = 16 and x2 + y2 = 4, shown below.
Calculate the volume of the solid which is inside of x2 + y2 + z2 = 16 but outside of x2 + y2 = 4.
32 3
11. Calculate the volume of the solid which is bounded above by z = 9 - x2 - y2, bounded below by z = 0, and contained within x2 - 3x + y2 = 0.
405 32
3
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- implementation american nurse
- worksheet logarithmic function
- practice book connecticut judicial branch
- sample exercise 14 1 calculating an average rate of
- official 2021 connecticut
- worksheet 14 practice exam 3 answer key
- title 14 public service corporations
- 14 3 ideal gases henry county schools
- lesson writing equations from tables 14 3 practice
- chapter 14 3 practice problems
Related searches
- sat math practice problems printable
- significant figures practice problems worksheet
- theoretical yield practice problems answers
- practice problems for significant figures
- synthesis practice problems and answers
- sig fig practice problems worksheet
- significant figures practice problems pdf
- act math practice problems printable
- nursing math practice problems printable
- chapter 14 lesson 4 cells and eneeryy gt
- chapter 14 alcohols exam style questions
- chapter 14 alcohol ms