Mathematics GRE

Hey can any solve this for me?

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

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.

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

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.

line integral was pretty straigt forward here.

and the ans I calculated is 2pi

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