Show that: [Use the geometric series to express ( e t 1 ) 1

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Show that:

sin t el dt -; H=I 1 n? +1

 [Use the geometric series to express (et1)1, observe that sint=Imeit and use Problem 10.9 .]

Data from problem 10.9

Integrating complex functions. Let (X, A, ) be a measure space. For a complex number z = x+iye C we write x =

Oc is generated by the balls in C.]

(ii) A map h: XC is A/C-measurable if, and only if, Reh and Imh are A/B(R)- measurable.

the maps z  (Rez, Imz) and (x, y) +z=x+iy are continuous.]

A function h: EC is called p-integrable, if Reh and Imh are u-integrable; we write L() for the complex

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