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

2. Originally Posted by bobby77
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
You need to know that:

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

so:

$x(t)=t^2-2$
$y(t)=(t-1)+t(t-2)cos(t)$.

Then

$\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 )

RonL