Advanced Placement Calculus AB covering limits, derivatives, and integrals.
Integrals are all about accumulation—adding up tiny pieces to find the whole. If derivatives break things down, integrals build them up!
An integral calculates the total area under a curve between two points. This can represent distance, total amount, or accumulated change.
The integral of \( f(x) \) from \( a \) to \( b \) is written as \( \int_a^b f(x),dx \).
The area under \( y = x \) from 0 to 2 can be found using an integral: \( \int_0^2 x,dx = 2 \).
To find how far you've traveled if you know your speed at every moment, integrate your speed over time.
Integrals find the total or the area under curves.