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sai govind Grade: 12
        

2f(x)+f(-x)=1/xsin(x-1/x).  find ∫f(x)dx in integral limits[e,1/e].

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear sai


2f(x)+f(-x)=1/xsin(x-1/x) .............1


replace x by -x


2f(-x)+f(x)=1/xsin(x-1/x).............2


2*(1) -(2)


 f(x) = (1/3x) sin(x-1/x)


s0   I =limit [e,1/e]  ∫f(x)dx


         =limit [e,1/e]   ∫(1/3x) sin(x-1/x)  dx ................3


nor let x=1/t


  dx=  -1/t2  dt


 I=limit [1/e,e]   ∫(1/3t) sin(t-1/t)  dx


or I=limit [e,1/e]   -∫(1/3x) sin(x-1/x)  dx ..............4


add 3 and 4


2I =0


I=0


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Badiuddin


 

7 years ago
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