Let
\[
I=\int_C z\,dx+y\,dy+xz\,dz,
\]
where \(x,y,z\) are real and \(C\) is the straight line segment from the point \((0,2,1)\) to the point \((4,1,-1)\). The value of the line integral \(I\) is
Show Hint
For line integrals over a straight line:
\[
\boxed{
\begin{aligned}
x&=x_1+(x_2-x_1)t,
y&=y_1+(y_2-y_1)t,
z&=z_1+(z_2-z_1)t,\qquad 0\le t\le1.
\end{aligned}
}
\]
Then substitute \(dx,dy,dz\) and integrate with respect to \(t\).