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Browse Classroom Capsules and Notes

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The author describes a method for identifying curves where the arc length is easy to compute by symbolic integration.

Certain identities that involve numbers from the Pascal triangle can be derived using Laplace transforms.

Use substitution to calculate partial fraction expansions

When the sample space is too small, then Bernstein's examples on independent events fail.

Use Green's Theorem to find a particular integral of a single variable

Describing Pythagorean Triples with one square side and a triangular side. Their number is infinite.

Generalized examples of a sphere and a circumscribing cylinder, which can also be used to calculate the surface area of a sphere.

Characterize positive integers which can be written as a sum of consecutive integers

Another approach to trisecting any acute angle

A new and elementary proof for a theorem in differential equations