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Mohsin007
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* The average value of an even function is (ve ,+ve, infinite, none)
 2 years ago
 2 years ago
Mohsin007 Group Title
* The average value of an even function is (ve ,+ve, infinite, none)
 2 years ago
 2 years ago

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vf321 Group TitleBest ResponseYou've already chosen the best response.1
Well that depends really... The average value of its entire domain?
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.1
I can think of an even function which has a finite average value, and I can think of one that has an infinite one...
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.1
If you were talking about an odd function then it'd be easy...
 2 years ago

Mohsin007 Group TitleBest ResponseYou've already chosen the best response.0
This was a question in my exam and i dnt knw how to figure it out..
 2 years ago

Mohsin007 Group TitleBest ResponseYou've already chosen the best response.0
What about an odd functon??
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.1
For an odd function it would be 0, since on the other side of the y axis you have negative values.
 2 years ago

Mohsin007 Group TitleBest ResponseYou've already chosen the best response.0
so the best ans is none...??
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.1
yes, I guess.
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.1
But to your previous question: For an odd function \(f\), we know that \(f(x)=f(x)\). As such, the average value (assuming \(f\) exists over all \(\mathbb R\)) is\[\lim_{a\rightarrow\infty}\frac{1}{2a}\int_{a}^af(x)dx=\lim_{a\rightarrow\infty}\frac{1}{2a}(\int_0^af(x)dx+\int_{a}^0f(x)dx))\]\[=\lim_{a\rightarrow\infty}\frac{1}{2a}(\int_0^af(x)dx+\int_{a}^0f(x)dx)\]Let \(u=x\)\[=\lim_{a\rightarrow\infty}\frac{1}{2a}(\int_0^af(x)dx\int_{0}^af(u)du)=0\]
 2 years ago
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