次の10問に挑戦願う。(ただし結果は明示的な式で示して下さい。)
[1]∫[x=0,∞] sin(x)/x dx
[2]∫[x=0,∞] sin(2*x)/x dx
[3]∫[x=0,∞] sin(3*x)/x dx
[4]∫[x=0,∞] (sin(x)/x)^2 dx
[5]∫[x=0,∞] (sin(x)/x)^3 dx
[6]∫[x=0,∞] sin^3(x)/x dx
[7]∫[x=0,∞] sin^3(x)/x^2 dx
[8]∫[x=0,∞] sin^5(x)/x dx
[9]∫[x=0,∞] (sin(2*x)/x)^3 dx
[10]∫[x=0,∞] (sin(3*x)/x)^3 dx
(コメント) WolframAlphaさんにお助けを乞うと、
[1] π/2 [2] π/2 [3] π/2 [4] π/2 [5] 3π/8 [6] π/4 [7] (3log3)/4
[8] 3π/16 [9] 3π/2 [10] 27π/8
となるらしいです。