Plot the graph of (x) = sin mx sin nx on [0, ] for the pairs (m,

Plot the graph of ƒ(x) = sin mx sin nx on [0, π] for the pairs (m, n) = (2, 4), (3, 5) and in each case guess the value of I = ∫^π₀ ƒ(x) dx. Experiment with a few more values (including two cases with m = n) and formulate a conjecture for when I is zero.