I had to evaluate an integral from 0 to 2pi in which the integrand was sqrt(sin(2x)^2). I figured the square root of sin(2x) squared was just sin(2x). Evaluating the integral gave me 0, which makes sense since the function is symmetric. But this was "incorrect".
Apparently sqrt(sin(2x)^2) = |sin(2x)|. How would I express the integral of the absolute value of a function? (Please generalize your answer so that it explains cases for which the function is not symmetric.)
|sin(2x)| = sin(2x) and -sin(2x) so would the integral of |sin(2x)| from 0 to 2pi be the sum of the integral of sin(2x) and the integral of -sin(2x) from 0 to 2pi?