Integration stops being a formula and starts being a shape. See the region fill in, the slices stack, and the solid spin — the geometry behind every area and volume integral.
One idea behind half the unit: an integral adds up a rate to give a total. Net change, motion, accumulation functions, and average value — taught as one.
Shade the region, sweep the representative strip, and see why you integrate in x or in y — including curves that cross more than once.
Stand squares, triangles, and semicircles up on a base region and watch them stack into a solid.
Spin a region around an axis into a real 3D solid. Disc and washer methods, around any line — grab it and rotate.
How long is a curve? Chop it into tiny hypotenuses and add them up — arc length is the Pythagorean theorem wearing an integral sign.
Mixed multiple-choice drawn from across the unit, plus full free-response problems in real AP format — the area-and-volume FRQ is an exam staple. A weak-spots tracker sends you back to whichever tool needs another look.
Go top to bottom. Start with Foundations for average value, motion, and accumulation, then Area, then the two volume tools. If you're in BC, finish with Arc Length. Each one builds on the integral-setup habit from the last.
Jump straight to whatever's shaky. Most students lose points on setting up area (dx vs dy) and on disc vs washer — the tools let you drill exactly those without re-reading the whole unit. The cheat sheet has every formula and the "which method?" logic on one printable page.