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.

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.