How do you solve this?

Question

Evaluate the line integral:

∫_c xzds where c is the line from (0,1, -1) and (2,0,1)

I started by solving for my r(t) which I found to be <2t, 1-t, -1> and 0 ≤ t ≤ 1. However, when I started plugging in my values for x(t), y(t), and ds, I ended up with the following

∫(2t)(-1)(√5)dt

I got an answer different from what my professor submitted (ultimately being 1)

Answer 1

I agree with your professor. The answer should be 1.

I think that your mistake is that r(t) should be < 2t ,1-t , -1 + 2t > , not what you wrote.

With that the length of the line segment is 3 not sqrt(5)