Calculus AB covers the fundamental concepts of differential and integral calculus, preparing students for advanced mathematical applications.
Integrals let us add up lots of tiny pieces to find totals—like finding the area under a curve or the distance traveled.
An integral finds the accumulation of quantities, like total distance from speed over time. It's the "opposite" of a derivative.
An antiderivative is any function whose derivative is the given function. If \( F'(x) = f(x) \), then \( F(x) \) is an antiderivative of \( f(x) \).
This theorem connects derivatives and integrals, showing they're two sides of the same coin!
Calculating the amount of rain that falls over a day or the fuel used on a road trip uses integration!
The integral of \( x \) from 0 to 2 is 2.
The antiderivative of \( 2x \) is \( x^2 + C \).
Integrals add up small changes to find totals, like areas or distances.