Suppose I have to evaluate the line integral of:
$\int_{c}xye^{yz}dy$
Where $c$ is parametrized by:
$x=t$, $y=t^2$, $z=t^3$, $0\leq t\leq1$
This gives me:
$\int_{0}^{1}2t^4e^{t^5}\sqrt{9t^4+4t^2+1} dt$
Correct so far? If so, I'm really stumped on how to integrate this, one idea I have is completing the square of the expression under the square root, but I'm not too sure.
Any help would be appreciated, thanks.
Actually it is much simpler: $$ \int_{c}xye^{yz}dy=\int_{c}0\,dx+xye^{yz}dy+0\,dz=\int_{0}^{1}2t^4e^{t^5} dt. $$