1. ## Line Integral

Evaluate $\int_Csinxdx+cosydy$ where C is the top half of the circle $x^2+y^2=4$ from (2,0) to (-2,0) and the line segment from (-2,0) to (-3,2).

Haven't done vector calc in awhile, still a little bit rusty, can someone assist me with getting the parametric equations for the line segment?

2. The line segment from $p_1$ to $p_2$ can be parametrized as $r(t)=(1-t)p_1+tp_2$, $0 \leq t \leq 1$.

3. Originally Posted by Em Yeu Anh
Evaluate $\int_Csinxdx+cosydy$ where C is the top half of the circle $x^2+y^2=4$ from (2,0) to (-2,0) and the line segment from (-2,0) to (-3,2).

Haven't done vector calc in awhile, still a little bit rusty, can someone assist me with getting the parametric equations for the line segment?

For the circle let

$x=2\cos{t}$ and $dx = -2\sin{t}$

$y =2\sin{t}$ and $dy = 2\cos{t}$

Now sub these values for

$\int_Csinxdx+cosydy$

and you get

$C_1 = \int^{\pi}_{0} \bigg(-2\sin{t}\sin{(2\cos{t})}+ 2\cos{t}\cos{(2\sin{t})}\bigg)dt$

For $C_2$

$x = -2 -t$ and $dx= -1$

$y =2t$ and $dy = 2$

and then just sub in like before.