Wednesday, 27 March 2019

calculus - Evaluating limbtoinftyintb0fracsinxx,dx=fracpi2











Using the identity limaa0extdt=1x,x>0,

can I get a hint to show that limbb0sinxxdx=π2.


Answer



Hint:
limbb0sinxxdx=lima,bb0a0extdtsinxdx=lima,bb0dta0exteixeix2idx=lima,bb0dta0e(ti)xe(i+t)x2idx

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