Homework Help: Evaluate the Line Integral

1. Dec 5, 2011

Bamboozled91

1. The problem statement, all variables and given/known data
Let C be the (positively oriented) boundary of the first quadrant of the unit disk. Use the definition of the line integral to find ∫(xy)dx+(x+y)dy

2. Relevant equations
x=rcos(x)
y=rsin(x)
dx=-sin(x)
dy=cos(y)
0≤ t ≤ ∏/2

3. The attempt at a solution
∫-cos(t)sin^2(t)+cos^2(t)+sin(t)cos(t) dt from 0 to ∏/2
Then I finished out the integral and was left with ∏/4-5/6 which is incorrect. Could it possibly have to do with the r or my limits of integration?

2. Dec 5, 2011

Bamboozled91

BTW I can do this using Greens theorem

3. Dec 5, 2011

Dick

No, the setup looks ok. I think you just did the integral wrong. I don't get the number you got as a answer.

4. Dec 5, 2011

Bamboozled91

I used wolfram to see where I mesed up and when it gave me the integral it gave the answer pi/4-1/6 which is also incorrect. Also another weird thing is I did the integral again and I got the same thing wolfram did unfortunatley the back of the book disagrees it says the answer is pi/4-1/3. Which I believe because I can solve using greens so you got anything else

5. Dec 5, 2011

Dick

You really need to show more of your work before we can help. Yes, Green's theorem gives you pi/4-1/3. So far you've only given the line integral over the arc. What do you get for the line integral over the x=0 and y=0 parts of the region?

6. Dec 6, 2011

Bamboozled91

Yah sorry about not showing too much work but that would require a ton of typing and I am lazy. Other than that, I think I have solved it. I found that the line integral over x=0 would cancel out. As for y=0, I determined it to be -1/2 so when I add -1/2 to pi/4+1/6. I get pi/4-1/3 which is correct. Let me show my work at least for the part I just did x=0 and y=t and dx = 0 and dy = 1 so I get ∫t dt from 1 to 0. which gives a -1/2

7. Dec 6, 2011

Dick

That's it all right.