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How to solve this line integral?

aruwin

Member
Jul 4, 2012
121
I have no idea how to even start with this problem. I know the basics but this one just gets complicated. Please guide me!


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!
 

Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,191
It looks to me as though you could define

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