I have this math problem, that I got a bit confused on. I just need to know whether or not I did it correctly. Thanks!
Question:
Calculate $\oint_c xe^{z}dx+yzdy+xe^{y}dz$ over the directed curve $C$ that is parameterized by $r(t) = t^2i+t^3j+t^4k$, $0\leq t \leq1$.
Work:
$r(t)=<t^2, t^3, t^4>$
$r'(t)=<2t, 3t^2, 4t^3>$
$x=t^2, y=t^3, z=t^4$
$dx=2t, dy=3t^2, dz=4t^3$
I plug into the equation: $\oint_c xe^{z}dx+yzdy+xe^{y}dz$
$\int_0^1 (t^2)e^{(t^4)}(2t)+(t^3)(t^4)(3t^2)+(t^2)e^{t^3}(4t^3) dt$
= $\int_0^1 2t^3e^{t^4} + 3t^9 + 4t^5e^{t^3} dt$
= $\frac{49+15(e-1)}{30}$
This is perfect my dear!! ;)
Now, you could vote again ;)