Question

If F = (3x^2 + 6y)i -(14yz)j + (20xz)k evaluate Integral(F)ds from (0,0,0) to (1,1,1) along the path c, from (0,0,0) to (1,0,0) to (1,1,0) to (1,1,1)

Answer 1

F dot r' sounds familiar to me

Answer 2

define the line in vector parts for x y and z (call it r); replace x y and z in F by their vector definitions; take derivative of r and dot it with F to get a more usual looking equation to integrate; and integrate it along the interval defined by the scalar on the vector

Answer 3

(0,0,0) to (1,1,1)

x = t
y = t
z = t
r = <t,t,t>, r' = <1,1,1>

t = 0 to 1

F = < 3x^2 + 6y, -14yz, 20xz >
F = < 3t^2 + 6t, -14t^2, 20t^2>

F.r' = 3t^2 + 6t -14t^2 + 20t^2

\[\int_{0}^{1}9t^2 + 6t~dt \]

Answer 4

You gave me a good idea of how i can tackle it... found the answer.. thanks.