1.

If `2f(x) - 3 f(1//x) = x," then " int_(1)^(2) f(x) dx` is equal toA. `(3//5)log2`B. `(-3//5)(1+log2)`C. `(-3//5)log2`D. None of these

Answer» Correct Answer - B
Given , `2f(x)-3f((1)/(x))=x`
Put `x=(1)/(x)` Eq . (i) , we get
`2f((1)/(x))-3f(x)=(1)/(x)`
On solving Eqs . (i) and (ii) , we get
`f(x)=-(3+2x^(2))/(5x)`
Now , `int_(1)^(2)f(x)dx=-int_(1)^(2)(3+2x^(2))/(5x)dx`
`=-int_(1)^(2)((3)/(5x)+(2x)/(5))dx`
`=(1)/(5)[3logx+(2x^(2))/(2)]_(1)^(2)`
`=-(1)/(5)(3 log2+4-2log1-1)`
`=-(1)/(5)(3log2+4-0-1]`
`=-(3)/(5)(1+log2)`


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