Question

The value of ${\int }_0^1{e}^{x^2-x}dx$ is

• A. < 1
• B. > 1
• C. > $e^{\frac{-1}{4}}$
• D. < $e^{\frac{1}{4}}$

Answer 1

Answer: (A), (C)

< 1
> $e^{\frac{-1}{4}}$

$I={\int }_0^1{e}^{x^2-x}dx$
For $0<x<1\Rightarrow -\frac{1}{4}<x^2-x<0$
$\Rightarrow e^{-1/4}<e^{x^2-x}<e^0\Rightarrow e^{-\frac{1}{4}}<{\int }_o^1{e}^{x^2-x}dx<1$