Post History
#2: Post edited
by
ziggurism
·
2023-01-06T13:40:14Z (almost 2 years ago)
A line integral is integrated with respect to arc length parameter. If the path you're integrating along is the $x$-axis, then the arc length parameter is just $x$, and so the integral is identical to an ordinary integral with respect to $x$.- You are right that it's a bit improper to write $f(x,0) = f(x)$, since the left-hand side is a two variable function with one variable evaluated at $y=0$, while the right-hand side is just a single variable function (though it may still be useful if you can tolerate some sloppiness).
- However I don't see anywhere that Stewart wrote such an equation.
- A line integral is integrated with respect to arc parameter. If the path you're integrating along is the $x$-axis, then the arc parameter can be taken to be just $x$, and so the integral is identical to an ordinary integral with respect to $x$.
- You are right that it's a bit improper to write $f(x,0) = f(x)$, since the left-hand side is a two variable function with one variable evaluated at $y=0$, while the right-hand side is just a single variable function (though it may still be useful if you can tolerate some sloppiness).
- However I don't see anywhere that Stewart wrote such an equation.
#1: Initial revision
by
ziggurism
·
2023-01-03T17:42:49Z (almost 2 years ago)
A line integral is integrated with respect to arc length parameter. If the path you're integrating along is the $x$-axis, then the arc length parameter is just $x$, and so the integral is identical to an ordinary integral with respect to $x$. You are right that it's a bit improper to write $f(x,0) = f(x)$, since the left-hand side is a two variable function with one variable evaluated at $y=0$, while the right-hand side is just a single variable function (though it may still be useful if you can tolerate some sloppiness). However I don't see anywhere that Stewart wrote such an equation.