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ok... so
we are given a function
\[\LARGE f(x) = x^3\] graphed between the intervals of -2 to 2

you wouldn't mind if we integrate first right? do you know anti-derivatives?

Hint : if \(f(x)\) is an odd function,
\[\int\limits_{-a}^a f(x)\,dx = 0\]

I dont mind, but negative on the anti derivatives (I think)

when we are taking the antiderivative, we add one to the exponent and divide by the new exponent.

so since your exponent is 3. What's 3 +1 ?

so do they mean, I am to look at the plot, and then work out the value of the integration equation?

hmmm.. 5-1?

j/k 4

|dw:1436955882543:dw|
now evaluate
f(b)-f(a)
or f(2)-f(-2)

but keep in mind we are restricted from -2 to 2 as well

Exactly!

The author of this program uses so many strange metaphors to me

so there is cancellation...

Indeed, the graph does give away the fact the the given function is "odd"
|dw:1436956075476:dw|

maybe the cancellations gave out the answer to that integral ?

gotcha, I haven't got to anti derivatives yet.. I think they're coming up.. and they just want me to look at the graph.. there's another identical one next..

another odd function... thanks to symmetry on the origin

same thing, just check if it is an odd one

hmmm, they might want me to do it analytically too..

I don't think we need integration by parts on this one... just u-substitution.

|dw:1436956504186:dw|

Well there is that f[-x] == -f[x] symmetry going on.

yeah, you must be telepathic

xD!

thank you for your instant help guys.. I dont think it was 30 seconds and you had me covered.

please someone approve usukiDoll for qualified helper status.

Good thing I didn't have wet polish otherwise I would have to do it over XD

there's also a test too.. that determines if the function is odd or not

for trigonometry , sinx cosx, tanx
sinx and tanx are odd functions
cosx is the only even function

erm.. you have to plug in -x in your x
and yes the definitions of odd and even functions help a lot.