...where curve C is given by the integral of (x^2)*y*sqrt(z)dz
C: x=t^3, y=t, z=t^2, t is between 0 and 1
I came up with the integral (from 1 to 0) (2t^12)*sqrt(1+9t^4+4t^2)
is this integral correct? if yes, how do I integrate it?
...where curve C is given by the integral of (x^2)*y*sqrt(z)dz
C: x=t^3, y=t, z=t^2, t is between 0 and 1
I came up with the integral (from 1 to 0) (2t^12)*sqrt(1+9t^4+4t^2)
is this integral correct? if yes, how do I integrate it?
I'm not sure what you're doing but you want the line integral
of (x^2)*y*sqrt(z)dz on the curve x=t^3, y=t, z=t^2 ?
F = (x^2)*y*sqrt(z) k
Since
x=t^3, y=t, z=t^2
F = t^6*t*t k = t^8 k
r = t^3 i + t j + t^2 k
r ' = 3t^2 i + j + 2t k
F*r ' = 2t^9
Which is easy to integrate over the interval 0 to 1