Question

If 5f(x) + 4f ($\frac{1}{x}$) = $\frac{1}{x}$+ 3, then $18\int_{1}^{2}$ f(x)dx is:

• A. 10 $l$n 3 - 6
• B. 5 $l$n2 - 6
• C. 10 $l$n 2 - 6
• D. 5 $l$n 2 - 3

Answer 1

Answer: (C)

10 $l$n 2 - 6

Answer 2

$5f(x)+4f(\frac{1}{x})=\frac{1}{x}+3......(i)$
Replace $x\rightarrow \frac{1}{x}$
$5f(\frac{1}{x})+4f(x)=x+3.....(ii)$
By (i) and (ii)
$9f(x)=\frac{5}{x}-4x+3$
$18\int_{1}^{2}f(x)dx=\int_{1}^{2}(\frac{10}{x}-8x+6)dx$
$18\int_{1}^{2}f(x)dx =$ 10 ln 2 - 6

So, the correct option is (C): 10 $l$n 2 - 6