Integrals of Symmetric Functions

If f(x) is continuous on [-a, a] and f is an even function, then

If f(x) is continuous on [-a, a] and f is an odd function, then

These properties of integrals of symmetric functions are very helpful when solving integration problems. Some of the more challenging problems can be solved quite simply by using this property.

Examples

Evaluate the definite integral of the symmetric function 

Solution:

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