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] = 2*integral(0,1) $x^2$*e^(-$x^2$) dx (even).