Question

The area enclosed between the curves $y=log(x+e);x=lo{g}_e\left(\frac{1}{y}\right)$ and x-axis is

• A. 3
• B. 1
• C. -2
• D. 0.222

Answer 1

The correct option is D 0.222

$e^y=-\ln y+e$

$e^y+\ln y=e$

${\int }_0^{0.642}\log (x+e)dx+{\int }_{0.642}^{\infty }{e}^{-x}dx$

$\left[x\log \right(x+e)-x{]}_0^{0.642}-[e^{-x}{]}_{0.642}^{\infty }$

$0.642\log (0.642+e)-0.642+e^{-0.642}$

$=0.222$