$\int_c z^2dx+x^2dy+y^2dz$
C is the line segment from (1,0,0) to (3,1,4)
My work:
$\int_c z^2dx+x^2dy+y^2dz$
x = 1 + 3t, dx = 3dt
y = t, dy = 1dt
z = 4t, dz = 4dt
I replaced the original x,y,z and dx,dy,dz
= $\int_0^1 (4t)^2*3dt+(1+3t)^2*1dt+(t)^2*4$dt
= $\int_0^1 48t^2dt+1+6t+9t^2dt+4t^2$dt
= $\int_0^1 61t^2+6t+1dt$
= $ \frac{61t^3}{3}+3t^2+t |_0^1$
= $ \frac{61}{3}+3+1 - (0)$
= $ \frac{61}{3}+4$
= $ \frac{61}{3}+\frac{12}{3}$
= $ \frac{73}{3}$
However this answer is wrong, and i'm not sure why.