Evaluate the line integral
ydx+x^2dy
where c=c1+c2.
C1 is the path of the straight line segment from the origin (0,0) to the point (4,23)
C2 is the path of the parabola y=-x^2+9x+3 from the point (4,23) to the point (7,17)

Question

Evaluate the line integral 
ydx+x^2dy
where c=c1+c2. 
C1 is the path of the straight line segment from the origin (0,0) to the point (4,23)
C2 is the path of the parabola y=-x^2+9x+3 from the point (4,23) to the point (7,17)

tkhunny · Answer

Should you parameterize the paths?

anonymous · Answer

When you parametrize you get x(t)=4t and y(t)=23t

anonymous · Answer

so dx=4dt and dy=23dt

tkhunny · Answer

Insufficient definition.  Specify for what values of t.
Also, how about the other one?

anonymous · Answer

What do you mean? and for C2 i get x(t)=4+3t and y(t)=23-6t

tkhunny · Answer

Insufficient definition. Specify for what values of t.

anonymous · Answer

C1: t is between 0 and 4
C2: t is between 4 and 7