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