Highlight of the Day: Context: AP Calc class, talking through some multiple choice (no calculator) problems from a practice test. Problem: what is ; Me (typical first question): So....what should we do? Student: Substitute the 2 in for t to find the answer Me: Why would we want to do that? Student: Well, f(x) is the integral there, which means it's really the anti-derivative of the function. We want the derivative of that anti-derivative, which basically means we want the stuff inside the integral. So if you just substitute 2 in, you'll get the answer. Me: You basically just explained the first part of the Fundamental Theorem of Calculus that you struggled with when we first talked about it. Woohoo! Granted, I know his explanation skips the step where t in the integrand becomes x after you take the derivative, but the conceptual understanding of the relationship between derivatives and integrals is there. Made my day.