# Julia - Green's theorem

Sorry, I did not see your question
=================================
Posted by julia on Monday, December 10, 2007 at 9:15pm.

Can someone show me step by step how to work this problem out please.

Let C be the triangle with vertices (0,0), (1,0), and (1,2). Find the following line integral by two methods, directly and using greens theorem.

2xy^2dx + yx^2dy

Thanks!!!

* Greens Theorem - Damon, Tuesday, December 11, 2007 at 6:35pm

directly
first from (0,0) to (1,0)
y = 0
x goes from 0 to 1
both terms are zero, so no contribution
second from (1,0) to (1,2)
Here dx = 0, x=1 and y goes from 0 to 2
so from 0 to 2 of y dy
= 2^2/2 = 2 total so far
now from (1,2) to(0,0)
dy = 2dx
y = 2x
so the integrand is
2 x (2x)^2 dx + 2x^3(2dx)
= 8x^3 dx + 4x^3 dx
= 12x^3 dx
from x = 1 to x = 0
3(0)^4 -3 (1^4) = -3
2 - 3 = -1 finally
NOW, using Green
closed path integral of Ldx+Mdy = integral over surface inside of
(dM/dx -dL/dy)
here L = 2xy^2
so dL/dy = 4xy
here M = y x^2
so dM/dx =2xy
so
dM/dx - dL/dy = integrand = -2xy
integral of
-2xy dy dx from y = 0 to y = 2x
then from x = 0 to 1
-2 *int x dx *int y dy
-2 * int x dx *[ y^2/2 from y = 0 to y = 2x]

-2 int x dx *2x^2

-4 int x^3 from 0 to 1

-4 (1^4/4) = -1

1. 👍 0
2. 👎 0
3. 👁 93

## Similar Questions

1. ### Algebra 2

Posted by Christian on Monday, May 7, 2007 at 11:34am. The area of a rectangular blanket in square centimeters is 40x^2+2x-65. The width is 4x-5 cm^2. Find the dimensions of the blanket in terms of x. For Further Reading Algebra 2

asked by Christian on May 7, 2007

I do not understand this question. Could you please explain? "Beneatha is particularly bitter, but Ruth defends Walter. What does Ruth say?" (Act III, SceneI) For Further Reading * A Raisin in the Sun - SraJMcGin, Monday,

asked by Anonymous on September 4, 2007

Posted by Anonymous on Sunday, September 2, 2007 at 6:01pm. download mp3 free instrumental remix Also a continued post from yesterday: I am wondering then why it's asked this way, "BENEATHA is particularly bitter, BUT Ruth defends

asked by Anonymous on September 3, 2007
4. ### Physics repost please check

Posted by Mary on Monday, November 5, 2007 at 8:19pm. A charged particle, passing through a certain region of space, has a velocity whose magnitude and direction remain constant. (a) If it is known that the external magnetic field

asked by Mary on November 6, 2007
5. ### English - Haiku reposted for Jean

English - jean, Monday, December 10, 2007 at 9:41pm What is the format to write a haiku?

asked by Ms. Sue on December 10, 2007
6. ### Physics repost please check

Posted by Mary on Monday, November 5, 2007 at 8:21pm. Suppose that the electric field of an electromagnetic wave decreases in magnitude. Does the magnetic field increase, decrease, or remain the same? Account for your answer. For

asked by Mary on November 6, 2007
7. ### algebra-Plz help

Posted by bailey on Monday, January 8, 2007 at 8:32pm. Posted by bailey on Monday, January 8, 2007 at 2:12pm. The area of a rectangular blanket in square centimetersis 40x^2+2x-65. The width is 4x-5cm^2. Find the dimensions of the

asked by bailey on January 9, 2007
8. ### Geography for CARIBE

Posted by CARIBE on Monday, September 10, 2007 at 4:17pm in response to MATHHHHHH. how many people are african in the world

asked by Ms. Sue on September 10, 2007
9. ### accounting

In 2007, Clyde Blackstock opened Clyde’s Pets, a small retail shop selling pet supplies. On December 31, 2007 Clyde’s accounting records showed the following: Merchandise inventory at December 31, 2007 \$10,250 Merchandise

asked by Anonymous on December 10, 2011
10. ### Science Reposted for Jessica

Posted by jessica on Monday, November 19, 2007 at 4:16pm in response to Science. is some friction good for life on earth??

asked by Ms. Sue on November 19, 2007

More Similar Questions