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Browse Classroom Capsules and Notes

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Displaying 141 - 150 of 225

Self-integrating Polynomials

Student error leads author to seek polynomials for which \(p(1)-p(0)\) equals the integral of \(p(x)\) on \([0,1]\).

How Do You Slice the Bread?

How do you cut a slice of bread (rectangle surmounted by an ellipse) into two "triangles" to equalize the areas?

Can You Paint a Can of Paint?

Author tries to resolve the paradox of the paint can that can be filled, but not covered with paint.

A Paradoxical Paint Pail

A new can, this one bounded, again has the property of having a finite volume, but an infinite surface area.

Differentiate Early, Differentiate Often!

Reasons are given for preferring implicit differentiation over eliminating a second variable, then differentiating.

Symmetry and Integration

Describes a symmetry-based technique for evaluating certain definite integrals

The Point-Slope Formula Leads to the Fundamental Theorem of Calculus

Approaches the fundamental theorem using piecewise linear functions.

The Spider's Spacewalk Derivation of sin' and cos'

Finds derivatives of trigonometric functions without using limits

A Generalization of the Mean Value Theorem for Integrals

Links mean value theorem with approximating sums for integrals

Finding Volumes with the Definite Integral: A Group Project

Discusses use of common objects (e.g., paper cups) in measuring volumes

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