(a) If g(x) = (sin2x)/x2, use your calculator or computer to make a table of approximate values of ∫t g(x) dx for t = 2, 5, 10, 100, 1000, and 10,000. Does it appear that ∫∞ g(x) is convergent?
(b) Use the Comparison Theorem with f(x) = 1/x2 to show that ∫∞ g(x) dx is convergent.
(c) Illustrate part (b) by graphing f and on the same screen for 1 < x < 10. Use your graph to explain intuitively why ∫∞ g(x) dx is convergent.