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

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
2I =0
I=0
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```
7 years ago
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