Even and Odd Functions: In Evaluating Definite Integrals

EVEN AND ODD FUNCTIONS
A function is said to be even if it will remain unchanged after replacing x by –x. Otherwise, it is an odd function.

Theorems on the integrals of even and odd functions when the limits are from –a to a:

If f(x) is an even function of x,

∫_(-a)^a▒f(x)dx = 2 ∫_0^a▒f(x)dx

If f(x) is an odd function of x,

∫_(-a)^a▒f(x)dx = 0