1. Vector field

Calculate the circulation of the vector field $\displaystyle F(x,y) = (x,xy)$ around the closed curve $\displaystyle x^2+y^2 = 25$ situated above the axis $\displaystyle OX$

2. we have talked before if F is a force field the line integral is the Work done

If F is a velocity field then the line integral is the circulation

so just compute the line integral of F over C

Her C consists of 2 parts the circle and the line segment along the x axis from -5 to 5

But of course you have Green's thm in your tool box as well

3. Originally Posted by Calculus26
we have talked before if F is a force field the line integral is the Work done

If F is a velocity field then the line integral is the circulation

so just compute the line integral of F over C

Her C consists of 2 parts the circle and the line segment along the x axis from -5 to 5

But of course you have Green's thm in your tool box as well
Above the axis ox:

$\displaystyle \int_0^{ \pi} (-costsent + cos^2tsent)dt = - \frac{2}{3}$

Correct ?

4. Not quite

x= 5cos(t) y = 5sin(t)

dr/dt = -5*sin(t) +5*cos(t)

F = 5cos(t)i +25cos(t)sin(t)

go from here

5. Originally Posted by Calculus26
Not quite

x= 5cos(t) y = 5sin(t)

dr/dt = -5*sin(t) +5*cos(t)

F = 5cos(t)i +25cos(t)sin(t)

go from here
$\displaystyle \int_0^{ \pi} (-25costsint + 125 cos^2tsint)dt = \frac{250}{3}$

It is correct ?

6. Ok--now you are correct----Again I've mentioned this before--slow down