find the integral of arctan(ax)dx on the interval from 0 to (1/a), where a is any positive number.  Use your result to show that the average value of arctan(ax) on the interval (0, 1/a) is always the same, no matter what value of "a" we choose.  What is that average value?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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find the integral of arctan(ax)dx on the interval from 0 to (1/a), where a is any positive number.  Use your result to show that the average value of arctan(ax) on the interval (0, 1/a) is always the same, no matter what value of "a" we choose.  What is that average value?

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