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Integrals : Even Functions and Integrability

Prove that if f(x) is even on [-a, a] and integrable on [0, a] where a>0, then f(x) is integrable on [-a, a] and Int([-a, a], f(x)dx) = 2*Int([0, a], f(x)dx).

Solution Preview

Since f(x) is even on [-a,a], then f(-x)=f(x).
f(x) is integrable on [0,a], then Int([0,a],f(x)dx)<oo.
Now I set ...

Solution Summary

Even functions and integrability are investigated.