Question

Evaluate
$ln( \binom{1}{n} ) {e}^{x} dx$
​

Answer 1

Question:-

$\large\rm { \displaystyle\int_{0}^{1} \ e^{x} \ dx}$

Answer:-

$\large\rm { = \displaystyle\int \ e^{x} \ dx}$ $\rm { \Bigg ( \displaystyle\int_{0}^{1} = \displaystyle\int \Bigg )}$

$\large { = e^{x}}$

$\large { = e^{1} - e^{0} }$

$\large\rm{\boxed{= e-1}}$

For further simplification , by putting value of $\bold{e }$ ,

${ e - 1 = 2.718281828 - 1}$

$\boxed{ e - 1 \approx 1.718281828}$

Values:-

$\large\rm { \displaystyle\int = \rm{ \ integral} }$

${ e = \rm { Euler's \ number \ (value \approx 2.718281828)}}$

Note:-

Here, " $\approx$ " denotes approx.