Need some help

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Need some help

legomyego180 · Answer

attachment

legomyego180 · Answer

would this be -3+3=0?

fwizbang · Answer

You technically have to divide by 10, but yes.

legomyego180 · Answer

why?

fwizbang · Answer

To get the average you divide by the length of the interval you integrated over

jim_thompson5910 · Answer

@legomyego180 
just as a side note, if they asked you for the average f(x) value on the interval [0,5], then 3/10 would be the correct answer

legomyego180 · Answer

oh right the formula

jim_thompson5910 · Answer

sorry not 3/10, it should be 3/5 since the interval width is 5 units long

legomyego180 · Answer

its not 
$$\frac{ 1 }{ 5-(-5) }\int\limits_{}^{}f(x)$$
?

jim_thompson5910 · Answer

but yes, since the function is odd, the integral from -5 to +5 is going to be 0

0/10 = 0 is your answer

legomyego180 · Answer

How does the function being odd affect it?

legomyego180 · Answer

And where does the zero come from?

jim_thompson5910 · Answer

If f(x) is an odd function, then
$$\Large \int_{-k}^{k}f(x)dx = 0$$
where k is some positive number

In this case, k = 5
$$\Large \int_{-5}^{5}f(x)dx = 0$$

legomyego180 · Answer

perfect thank you

jim_thompson5910 · Answer

The symmetry has one half of the function cancel out with the other half example: http://www.emathhelp.net/images/sol/217.png the pink portion (negative area) cancels out with the green portion (positive area)

legomyego180 · Answer

@jim_thompson5910 justr curious how do you know all of this?

jim_thompson5910 · Answer

just a lot of practice