50. (a) Integrating by parts twice (see Example 4), find fsin ax cos bx dx, where a # b2. (b) Using the formula sin 2x = 2 sin x cos x, find [sin ax cos bx dx when a = + b. (c) Let g(a) = (4/w)fg sin x sin ax dx. Find a formula for g(a). (The formula will have to distinguish the cases a* * 1 and a? = 1.) (d) Evaluate g(a) for a = 0.9, 0.99, 0.999, 0.9999, and so on. Compare the results with g(1). Also try a = 1.1, 1.01, 1.001, and so on. What do you guess is true about the func- tion g at a = 1