Integration & Area Explorations
Area Under a Curve
Ever wonder how much space is under a wiggly line? We use math to find exactly how much 'ground' a function covers!
Riemann Sums (Left/Right)
Before we had these math formulas, we used tiny rectangles to estimate areas. It’s like building a puzzle piece by piece!
Definite Integrals as Area
This is the official tool for finding the exact area between two points on a graph. No more guessing with rectangles!
Indefinite Integrals & Antiderivatives
Think of this as 'un-doing' a derivative. It's like finding the original recipe after looking at the finished cake!
Fundamental Theorem of Calculus (Parts 1 & 2)
The bridge that connects slope-finding (derivatives) with area-finding (integrals). It's the 'Grand Finale' of Calculus!
Basic Integration Rules
Just like addition and subtraction, integration has its own set of easy rules to follow. Master these and you’re a math wizard!
u-Substitution
When a math problem looks too scary, we swap out the messy parts with a simple letter 'u' to make it easy to solve.
Area Between Two Curves
What happens when two wiggly lines cross? We calculate the space trapped right in the middle!
Average Value of a Function
Graphs go up and down, but what’s the middle ground? We find the 'level' height of a function over time.
Accumulation Functions
This tracks how things pile up over time, like water filling a tub or points adding up in a game.
Net Change and Integrals
If you go forward and backward, where do you actually end up? We calculate the final result of all that moving around.
Integration in Motion Problems
From rockets launching to cars braking, integration tells us exactly how far we’ve traveled based on our speed.