Each card is a single, complete idea: what it is, the formulas you need, and one worked example. Built to be re-read.
Integrate top minus bottom for vertical slices, or right minus left for horizontal slices.
Find the area of one geometric slice, then integrate that area across the base region.
Rotate a region about an axis: use discs when the region touches the axis, washers when a hole is created.
For a function continuous on [a, b], the average value is the height of a rectangle with the same area as the region under the curve.
Integration moves backwards through motion: velocity is an antiderivative of acceleration, and position is an antiderivative of velocity.
The definite integral of a rate function gives the net change in the quantity over that interval — the backbone of calculator-active free response.