Question

The area bounded by the curve $y=2^x$, the $x$-axis and $y$-axis is:

• A. ${\log }_{e}2$
• B. ${\log }_{e}4$
• C. ${\log }_{4}e$
• D. ${\log }_{2}e$

Answer 1

Answer: (D)

${\log }_{2}e$

The area bounded, as shown in figure
$={\int }_{-\infty }^0{2}^{x}dx$
$={\int }_{-\infty }^0{e}^{xln2}dx$
$=\frac{e^{xln2}}{ln2}{|}_{-\infty }^0$
$=\frac{1}{ln2}$