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Topic: Seeking Beautiful Single-Variable Calculus Problems
Replies: 8   Last Post: Jul 16, 2006 2:35 PM

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Karl M. Bunday

Posts: 127
Registered: 12/6/04
Re: Seeking Beautiful Single-Variable Calculus Problems
Posted: Jul 16, 2006 2:32 PM
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Ken wrote, providing information I sought:

> This classic little fallacious argument may be too easy for them.
>
> Since x^2 is positive, you would expect
>
> the integral from -1 to +1 of 1/(x^2) dx
>
> to be positive. However, the usual calculation using an antiderivative
> gives
>
> [-1/x] from -1 to +1
>
> = - 1 - (- (- 1))
>
> = - 2 which is negative.
>
> Why?


I appreciate the problem. Thanks for your help.

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Karl M. Bunday P.O. Box 1456, Minnetonka MN 55345
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