Line Integral and Greens Theorem

I'm supposed to do the following problems, first using line integrals and then Green's theorem....but I keep getting different answers. Can someone please help me see my error? Thanks.

1a) Let C be the positively oriented boundry of the first quadrant part of the unit disk. Use the definition of the line integral to find:

My Work:

b/c it is only in the first quadrant

1b) Now using Green's Theorem:

Re: Line Integral and Greens Theorem

Quote:

Originally Posted by

**dbakeg00**

not .

..

Green's theorem says that area integral is equal to the integral of your first function over the **entire** boundary of the region. That includes the integral from (0, 0) to (1, 0) along the x-axis and the integral from (0, 1) to (0, 0) along the y-axis.

Re: Line Integral and Greens Theorem

So are you saying my bounds are wrong? I see that I have a typo on the double integrals bounds, they should have read 0 to 1.What should my bounds be?

Re: Line Integral and Greens Theorem

No, I am saying that your path integral is not around the entire boundary of the region!

Re: Line Integral and Greens Theorem

I now see what you meant...I only covered the arc portion in my first attempt. When I included the axis portions, I ended up getting the same asnwer as I did using Green's Theorem. Thanks for the help.