(Solution Download) If t 0 define E t 0 e txsin x x dx a

If t > 0, define E(t) := ??0 [(e-txsin x)/x]dx .
(a) Show that E exists and is continuous for t > a > 0. Moreover, E(t) ? 0 as t ? ?.

(c) Deduce that E(t) = 1/2 ? - Arctan t for t > 0.
(d) Explain why we cannot use the formula in (c) to obtain equation (12).

 

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