Thread: Line integral parameters

I'm looking at an example in my notes where the line integral of two segments is being evaluated so (integral)C=(integral)C1+(integral)C2.

For c1 : segment between (0,0) and (1,1)
For c2: part of the parabola y = sqrt(x) between (1,1) and (4,2)

for the parameterization it's written:

c1: x(t) = t, y(t) = t, 0<=t<=1
c2: x(t) = t², y(t) = t, 1<=t<=2

Can someone explain to me how to get that parameterization?

anyone?

http://tutorial.math.lamar.edu/Class...egralsPtI.aspx

For segment C1, just use the line segment to vector equation:

r(t) = (1-t)<Xo, Yo> + t<X1, Y1> where Xo,Yo are the starting points (0,0) and X1 and Y1 are the ending points (1,1).

For segment C2, note:

y = sqrt(x), so x = y^2. Thus, you can use y as the parameter.

y = t, x = t^2, and y goes from 1 to 2.


hope this helps