Find line integral F(x,y) .dr

where C is the curve given by

r(t)=(t^2 -2)i+((t-1)+t(t-2)cos(t))j 0<=t<=2

and

f(x,y) = (xy^2+2x)i+(x^2y +y+1)j

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- Dec 8th 2005, 09:44 PMbobby77line integral very urgent please help
Find line integral F(x,y) .dr

where C is the curve given by

r(t)=(t^2 -2)i+((t-1)+t(t-2)cos(t))j 0<=t<=2

and

f(x,y) = (xy^2+2x)i+(x^2y +y+1)j - Dec 9th 2005, 04:27 AMCaptainBlackQuote:

Originally Posted by**bobby77**

$\displaystyle \vec r(t)\ =\ x(t).i\ +\ y(t).j$

so:

$\displaystyle x(t)=t^2-2$

$\displaystyle y(t)=(t-1)+t(t-2)cos(t)$.

Then

$\displaystyle \int_C{\vec F(x,y)} \cdot d \vec r\ =\ \int_0^2{\vec F(x(t),y(t))} \cdot \frac{d \vec r}{dt}\ dt\ $

which I trust you I can leave to you ;)

(by the way the value of the integral is 2 :D )

RonL