PYQ Vault
EbooksTutor

f(x) = integral from 1 to x of log t/(1 + t): find f(a) + f(1/a)

The same question, asked 2 times: 2021 Paper 26*, 29 Jul 2022. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 26

    73
    For x>0x > 0, if f(x)=∫1xlog⁡et(1+t)dtf(x) =\int_{1}^{x} \frac{\log_{e}t}{(1 + t)}dt, then f(e)+f(1e)f(e) + f\left( \frac{1}{e} \right) is equal to:

    Tap an option to check your answer.

  2. Question 2

    29 Jul 2022

    75
    If f(α)=∫1αlog⁡10t1+tdt,α>0f(\alpha) =\int_{1}^{\alpha} \frac{\log_{10}t}{1 + t}dt,\alpha > 0, then f(e3)+f(e−3)f\left( e^{3} \right)+ f\left( e^{- 3} \right) is equal to :

    Tap an option to check your answer.