- Thread starter
- #1

Find the line integral:

∫C {(-x^2 + y^2)dx + xydy}

When 0≤t≤1 for the curved line C, x(t)=t, y(t)=t^2

and when 1≤t≤2, x(t)= 2 - t , y(t) = 2-t.

Use x(t) and y(t) and C={(x(t),y(t))|0≤t≤2}

Help!

- Thread starter aruwin
- Start date

- Thread starter
- #1

Find the line integral:

∫C {(-x^2 + y^2)dx + xydy}

When 0≤t≤1 for the curved line C, x(t)=t, y(t)=t^2

and when 1≤t≤2, x(t)= 2 - t , y(t) = 2-t.

Use x(t) and y(t) and C={(x(t),y(t))|0≤t≤2}

Help!

- Admin
- #2

- Jan 26, 2012

- 4,198

$$C_{1}:\quad 0\le t\le 1,\quad x=t,\quad y=t^{2},$$

and

$$C_{2}:\quad 1\le t\le 2,\quad x=2-t,\quad y=2-t.$$

You're asked to compute

$$\int_{C}=\int_{C_{1}}+\int_{C_{2}}.$$

Where do you go from here?