JEE Advance - Mathematics (1996 - No. 9)
If for nonzero $$x$$, $$af(x)+$$ $$bf\left( {{1 \over x}} \right) = {1 \over x} - 5$$ where $$a \ne b,$$ then
$$\int_1^2 {f\left( x \right)dx} = .......$$
$$\int_1^2 {f\left( x \right)dx} = .......$$
$$\frac{1}{a^2 - b^2} \left[ a(\log 2 - 5) + \frac{7b}{2} \right]$$
$$\frac{1}{a^2 + b^2} \left[ a(\log 2 + 5) - \frac{7b}{2} \right]$$
$$\frac{1}{a - b} \left[ a(\log 2 - 5) + \frac{7b}{2} \right]$$
$$\frac{1}{a + b} \left[ a(\log 2 - 5) - \frac{7b}{2} \right]$$
$$\frac{1}{a^2 - b^2} \left[ b(\log 2 - 5) + \frac{7a}{2} \right]$$
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