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Math · Advanced

Calculus: Integrals

Slice areas into thinner and thinner rectangles, discover that integration undoes differentiation, use integrals to find distances, averages, volumes and the work done by a force, and tame regions that stretch out to infinity.

7 lessons~40 min0/7 complete
1

Area Under a Curve

Approximate with rectangles, then take the limit.

  1. RectanglesRiemann sums
  2. Signed AreaAbove counts plus, below counts minus
2

The Fundamental Theorem

Integration undoes differentiation.

  1. AntiderivativesRunning derivatives backwards
  2. The Fundamental TheoremAreas from antiderivatives
3

Using Integrals

Averages, areas and physics.

  1. Integrals at WorkAverages, areas between curves, work
4

Beyond Area

Volumes, and regions that go on forever.

  1. Volumes by SlicingStacks of thin disks
  2. Infinite AreasWhen infinity adds up to something finite

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