## FR0568 #41

Forum for the GRE subject test in mathematics.
thmsrhn
Posts: 17
Joined: Fri Mar 26, 2010 7:18 am

### FR0568 #41

Hey can any solve this for me?

I know how to solve the line intergral, but what are the upper and lower limits?

origin415
Posts: 61
Joined: Fri Oct 23, 2009 11:42 pm

### Re: FR0568 #41

When you make new threads like this, please post the problem to make it easier for everyone.

The question is
Let C be the circle $$x^2 + y^2 = 1$$ oriented counterclockwise in the xy-plane. What is the value of the line integral
$$\oint_C (2x-y) dx + (x+3y)dy$$

A) 0
B) 1
C) pi/2
D) pi
E) 2pi

The limits you need for the integral will depend on the parametrization of the circle you use. You could use the parametrization $$y = \sqrt{1-x^2}$$ for the top half of the circle, and then your x would go from 1 to -1. You'll also need to compute the integral on the bottom half.

However, I think actually attempting to compute that line integral would be excessively difficult and miss the point of the question, use the other techniques at your disposal.

thmsrhn
Posts: 17
Joined: Fri Mar 26, 2010 7:18 am

### Re: FR0568 #41

God it s hard integrating this line integral, have you got another method in mind origin? Coz I could sure it rite now.

origin415
Posts: 61
Joined: Fri Oct 23, 2009 11:42 pm

### Re: FR0568 #41

And spoil all the fun of it?

Alright, Green's Theorem.

Basically anytime you have a surface integral, you should be checking if its easier to integrate the boundary, and anytime you have a closed line integral, you should be checking if its easier to integrate the surface. The GRE guys are tricky like that.

mathQ
Posts: 41
Joined: Thu Mar 25, 2010 12:14 am

### Re: FR0568 #41

line integral was pretty straigt forward here.

and the ans I calculated is 2pi

thmsrhn
Posts: 17
Joined: Fri Mar 26, 2010 7:18 am

### Re: FR0568 #41

hey greens theorem did the trick! Hardly took any time!! thanks!!!