Solved: If t > 0, define E(t) := fooo[(e-'Xsinx)lx] dx.(a) Show that E exists and is
Chapter 10, Problem 10(choose chapter or problem)
If t > 0, define E(t) := fooo[(e-'Xsinx)lx] dx.(a) Show that E exists and is continuous for t > a > O.Moreover, E(t) ~ as t ~ 00.I0 (e-1X sin X)I-1(b) Since -ot x ~ e-ax for t 2:a > 0, showthatE'(t) = t~ + 1 for t > 0.(c) Deduce that E(t) = !1r - Arctant for t > O.(d) Explain why we cannot use the fonnula in (c) to obtain equation (12).
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