The biggest unit in BC — where adding up infinitely many slivers becomes exact area, and differentiation meets its inverse. Five interactive tools that turn Riemann sums, the Fundamental Theorem, and every integration technique into things you can watch happen.
Work them in order for a full walkthrough of the unit, or jump straight to whatever's giving you trouble.
Where integration begins: a rate accumulates into a total, and rectangles under a curve close in on exact area. Left, right, midpoint, and trapezoid — drag the count up and watch every one of them converge to the same number.
The hinge of all of calculus. Build the accumulation function g(x) = ∫f by sweeping area, watch why its derivative is f itself, and use both parts of the FTC to evaluate definite integrals and read accumulation graphs.
Running derivatives in reverse. The basic antiderivative rules, then u-substitution — the chain rule undone — plus the algebraic setup moves: long division and completing the square turn ugly integrands into ones you know.
The two BC-only weapons. Integration by parts — the product rule undone — with the tabular method as the fast lane for repeated rounds, and partial fractions for splitting rational integrands into pieces that integrate to logs.
Integrals that run to infinity — or across a point where the function blows up. Replace the bad endpoint with a limit and watch the area either settle to a finite value or grow without bound. The gateway to Unit 10’s series.
Put it together the way the real BC exam does — mixed multiple choice first, then full integration free-response.
You pick the approach: mixed multiple choice across all fourteen topics with worked explanations and a weak-spot finder, plus chained free-response in the classic BC integration mold — Riemann estimates from a table, accumulation functions, and the BC-only techniques.
Begin practicing →From rectangles closing in on exact area, through the Fundamental Theorem, u-substitution, integration by parts, and partial fractions, to integrals that run to infinity — and a capstone that mixes it all together the way the real exam does. Everything verified, nothing hand-wavy.