16 - Function Symmetry in Integrals - Odd Functions

We define a function of odd symmetry as symmetrical with respect to the origin:
Consider the following:
center

Notice the graph.

The surfaces from to are opposites, so they'll cancel each-other out.
This looks like they would level each-other out.

So what would this integral be, without calculating it, but just looking at the graph?
If you thought zero, that's a pretty reasonable and obvious guess.

Well, is it the case?

Let's prove it.

You have proven the integral of an odd function for a symmetric interval:

Well done!

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