Question

Line Integrals:
Integrate F(x,y,z)=x+y^1/2-z^2 over the path from (0,0,0) to (1,1,1)
C1UC2
C1 r(t)=ti+t^2j from 0 to 1
C2 r(t)=i+j+tk from 0 to 1

Cannot get the correct answer. Help me find my mistake.

Answer 1

Did you parameterize the line segment correctly, using (1-t)<ro> +t<r1> . I'm pretty sure that is the first step. Line integrals confuse me. I'll definitely be hitting the books this weekend.

Answer 2

Yes, did that. but their answer and mine are way off.

Answer 3

I beleive the formula is int from a to b f(x,y,z)ds

Answer 4

translates to int 0 to 1, (t,t^2,0)(2^1/2)dt

Answer 5

+ int 0 to 1 f(1,1,t)(1)dt

Answer 6

first integral I get 2^1/2

Answer 7

second integral i get 5/3+2^1/2

Answer 8

Don't take my word for it. but I think the first step would be to find the line integral of c1, which would be f(r(t) (dot)r'(t) dt. I think this is what it should look like


\[\int\limits\limits_{0}^{0}1+t * \sqrt{1^2 +(2t)^2 dt}\]

Possibly?

Answer 9

is that not a vector field? instead of a line integral?

Answer 10

err, I think you are right. aha :[ Maybe someone with more knowledge should answer this.

Answer 11

thanks anyways, I'm going to press on.

Answer 12

Did you get this?
\[\frac{1}{6} \left(11+5 \sqrt{5}\right)\]