DEFINITE INTEGRAL | PROPERTIES OF DEFINITE INTEGRALS, SOME SPECIAL RESULTS | Property 9: If f(x) is a continuous function defined on `[-a; a]` then `int_(-a) ^a f(x) dx = 0` if f(x) is odd and `2 int_0 ^a f(x) dx` if f(x) is even, Examples: `int_(-pi/2) ^(pi/2) sin^2x dx`, Property 10: If `f(x)` is a continuous function defined on `[0, 2a]` then `int_0 ^(2a)f(x)dx = 2 int_0 ^a f(x) dx`; if `f(2a-x) = f(x)` and 0 if `f(2a-x) = -f(x)`, Examples: `int_(-1) ^1 e^|x|dx`, Examples: `int_(-pi/2) ^(pi/2) (x sinx) / (e^x + 1) dx`, Examples: `int_0 ^(2pi) cos^5x dx`, Integration of `Sinx` in different range, Integration of `sin^2x` or `cos^2x` in different range, `int_0 ^(pi/2) log sinx dx = int_0 ^(pi/2) log cosx dx = 1/2 (pi) log(1/2)`