15 - Function Symmetry in Integrals - Even Functions

Knowing if a function is even or odd helps us a great deal in integrals.

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We know that the cosine is even.

That is,

First, calculate that definite integral.

This tells us that the area under the curve of cos(x) is equal to 2.

Now notice the graph.

The cosine is y-symmetrical (even). That means cos(-x) = cos(x).
Try to visualize folding this graph in two across the y-axis.

You easily figure it out.

The integral of an even symmetrical curve:

Try proving it!

Et voila.

Now what if we had an odd function instead? You probably have already figured it out, or have an idea.

And I'm proud of you for that. Let's go.

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