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Mohsin007
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* The average value of an even function is (ve ,+ve, infinite, none)
 one year ago
 one year ago
Mohsin007 Group Title
* The average value of an even function is (ve ,+ve, infinite, none)
 one year ago
 one year 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?
 one year 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...
 one year 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...
 one year 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..
 one year ago

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

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

vf321 Group TitleBest ResponseYou've already chosen the best response.1
yes, I guess.
 one year 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 \(u=x\)\[=\lim_{a\rightarrow\infty}\frac{1}{2a}(\int_0^af(x)dx\int_{0}^af(u)du)=0\]
 one year ago
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