Even function: f(-x) = f(x). Graph symmetric about y-axis. integral(-a to a) f(x) dx = 2 * integral(0 to a) f(x) dx

Odd function: f(-x) = -f(x). Graph symmetric about origin. integral(-a to a) f(x) dx = 0

How to identify:

• x^2, |x|, cos x, x^2 sin^2 x are even
• x, x^3, sin x, xcos x, xe^(x^2) are odd
• Product rules: eveneven = even, oddodd = even, even*odd = odd

JEE Trap: x^3 * e^(-x^2) on [-1,1] = 0 (odd). But x^2 * e^(-x^2) on [-1,1] = 2integral(0,1) x^2e^(-x^2) dx (even).