Definite integrals of symmetric functions
Definite integration · Mathematics
Study notes
Q: Evaluate (a) the integral from -2 to 2 of x^3 dx, (b) the integral from -2 to 2 of x^2 dx. (a) x^3 is odd: f(-x) = -f(x). Symmetric limits, so the integral is 0 - left cancels right! (b) x^2 is even: integral = 2 times the integral from 0 to 2 of x^2 dx = 2(8/3) = 16/3.