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 $\displaystyle OX$

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- Apr 27th 2009, 07:03 AMApprentice123Vector fieldCalculate 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 $\displaystyle OX$
- Apr 27th 2009, 10:13 AMCalculus26
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 - Apr 27th 2009, 10:42 AMApprentice123
- Apr 27th 2009, 11:11 AMCalculus26
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 - Apr 27th 2009, 11:20 AMApprentice123
- Apr 27th 2009, 11:28 AMCalculus26
Ok--now you are correct----Again I've mentioned this before--slow down

and take your time - Apr 27th 2009, 11:31 AMApprentice123