Continuously Differentiable Functions with Compact Support
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Let f : [0,∞)-->R be continuously differentiable with compact support in [0,∞); and 0<a<b<∞. Prove that:
∞
∫ [f(bx)-f(ax)]/x dx = -f(0) ln (b/a)
0
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Problem:
Let be continuously differentiable with compact support in [0, +) and 0 < a < b < .
Prove that
Solution:
We consider the following integral with parameters:
(1)
Since f = differentiable, we can ...
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