Line Integral

[Weatherkid11]

Find the exact value of

where

and C is the line segment from (1,2,1) to (6,4,5).
i, j, k are unit vectors

So far all i have done is drawn in the line segment on a 3D graph..

 

[galactus]

We must find parametric equations which trace the path of integration.

\(\displaystyle (1-t)r_{0}+tr_{1}\)

\(\displaystyle (1-t)[1,2,1]+t[6,4,5]\)

\(\displaystyle =[5t+1,2t+2,4t+1]\)


\(\displaystyle \int_0^{1}((5t+1)^{4}e^{2t+2}(5)+ln(4t+1)(2)+sqrt{(2t+2)^{2}+(4t+1)^{2}}(4))dt\)

Check my work, please. This seems like a monster of an integral to solve without the help of a computer/calculator.

 

[Weatherkid11]

Thank you thank you!