E1: Choose cosx in the comboBox. It will be calculated and displayed in red. Activate the Integral check box. The integration process will begin with the initial value of the function at x = 0 and will progress in blue to the end of the fundamental period x = 2 π. Reflect why the end value and hence the definite integral over the interval is zero
E2: Change index n with the slider and watch the integral curve. Reflect again why the definite integral is always zero.
E3: Choose sinx and verify the experiments for it.
E4: Choose asinx + bcosnx and assure yourself by varying a, b, n that the superposition is always a simple, phase shifted periodical, whose definite integral is zero.
E5: Choose cosx * sinx and assure yourself that the definite integral is always zero.
E6: Choose the remaining "mixed" functions and assure yourself that the definite integral is non zero only when both terms are of the same type and have identical indices.
E7: Integrate some of the functions analytically and verify the experimental findings.
E8: Conclude in general which characteristics of the functions sine and cosine are the base of your results.