# Just an Average Integral

by John Frohliger (St. Norbert College) and Rick Poss (St. Norbert College)

This article originally appeared in:
Mathematics Magazine
October, 2008

Subject classification(s): Calculus | Single Variable Calculus | Integration
Applicable Course(s): 3.2 Mainstream Calculus II | 3.6 Differential Equations

The antiderivative of the cube of the secant function is the average (arithmetic mean) of the derivative and antiderivatives of the secant function. That is, what are the solutions of $$\int y^3 dx= 1/2 (y' + \int y$$ $$dx)$$?

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Capsule Course Topic(s):
One-Variable Calculus | Differential Equations (for Calculus)
Ordinary Differential Equations | Analytic Methods