First slide

Properties of ITF

Question

If $f (x) = {(\tan^{- 1} x)}^{3} + {(\cot^{- 1} x)}^{3}$ and the range of $f (x)$ is [a, b] then ${(\frac{b}{7 a})}^{3}$ is

Moderate

Solution

$b = \frac{7 π^{3}}{8},$ $a = \frac{π^{3}}{32}$ $\Rightarrow {(\frac{b}{7 a})}^{3} = {(\frac{\frac{7 π^{3}}{8}}{\frac{7 π^{3}}{32}})}^{3} = 64$

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