Is Integral Curves Like Contours?

In multivariable, we're now thinking about it as a graph itself. Instead of projecting it onto a contour map, which what we did in multivariable,. We're now think about it as an integral curve and that will define your solution. If you were to have a graphs, the way to visualize that three dimensional graph would be to draw the lines where your function is constant and then project it down. But here, we're telling you what the contours look like, and then your job is to bring it out into three dimensions.