Question

The area enclosed between the curve $y={\log }_e(x+e)$ and the coordinate axes is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A $1$

A]$A={\int }_{1-e}^{0}ln(x+e)dx$

$={\int }_{1-e}^0{x}^{0}ln(x+e)dx$

= $\left(xln\right(x+e\left)\right)-{\int }_{1-e}^0\frac{x}{x+e}dx$

= $-{\int }_{1-e}^0\frac{x+e-e}{x+e}dx$

$={\int }_{1-e}^0\left(\frac{e}{x+e}\right)dx$

$=\left[eln\right(x+e)-x{]}_{1-e}^0=1$