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Just an Average Integral

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 \(\int y^3 dx= 1/2 (y' + \int y\) \(dx)\)?

Old Node ID: 
1852
Author(s): 
John Frohliger (St. Norbert College) and Rick Poss (St. Norbert College)
Publication Date: 
Thursday, June 5, 2008
Original Publication Source: 
Mathematics Magazine
Original Publication Date: 
October, 2008
Subject(s): 
Calculus
Single Variable Calculus
Integration
Topic(s): 
Differential Equations (for Calculus)
Analytic Methods
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Furnished by JSTOR: 
File Content: 
Rating Count: 
22.00
Rating Sum: 
67.00
Rating Average: 
3.05
Author (old format): 
John Frohliger and Rick Poss
Applicable Course(s): 
3.2 Mainstream Calculus II
3.6 Differential Equations
Modify Date: 
Monday, August 20, 2012
Average: 3.1 (22 votes)

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