So I can’t quite decide what to call integration/antidifferentiation in the notes. I have always used integrate with the understanding that it means to compute the Riemann integral and thereby compute the antiderivative by FTC. That is, writing the indefinite integral as a shortcut for the actual integral:
But it seems that when students hear “integrate” they really think just of symbolic antidifferentiation. I could change all instances of “integrate” to “antidifferentiate.” But in places it just sounds bad. I feel like I want to actually integrate at places because I want to “compute” the actual functions. To me “antidifferentiation” smells of trying to get a closed form expression in terms of elementary functions or some such. As an analyst I want to always just “integrate.”
Also if I change to the word “antidifferentiate,” then the whole “integrating factor method” sounds off.