# Homework Help: Integrals 4

1. Jan 25, 2012

### bugatti79

1. The problem statement, all variables and given/known data

Use Green's Theorem to calculate $\int F dr$

2. Relevant equations

$F(x,y)= (\sqrt x +y^3) i + (x^2+ \sqrt y) j$ where C is the arc of y=sin x from (0,0) to ( pi,0) followed by line from (pi,o) to (0,0).

3. The attempt at a solution

We have $\int f dx + g dy = \int \int_R (g_x-f_y)$ dA for counterclockwise rotation, but the question is given in clockwise rotation so does green's theorem become

$- \int \int_R (g_x-f_y) dA$...? Ie, a sign change?

2. Jan 26, 2012

### bugatti79

Any clues on this one?

Thanks

3. Jan 26, 2012

### SammyS

Staff Emeritus
Yes, clockwise gives the opposite sign compared to counter-clockwise.

4. Jan 26, 2012

### bugatti79

Thanks

5. Jan 26, 2012

### bugatti79

Can anyone confirm this integral is set up correctly?

$\displaystyle \int_0^ {\pi} \int_0^ {sin x} (3y^2-2x) dy dx$

6. Jan 26, 2012

### SammyS

Staff Emeritus
That looks OK to me.