Question

The value of the integral ${\int }_0^1{e}^{x^2}dx$

• A. is less than $1$
• B. is greater than $1$
• C. is less than or equal to $1$
• D. lies in the closed interval $[1,e]$

Answer 1

The correct option is B is greater than $1$

$e^x>1,\forall x\in (0,1)\therefore e^{x^2}>1,\forall x\in (0,1)\Rightarrow {\int }_0^1{e}^{x^2}dx>\underset{0}{\overset{1}{\int }}1dx=1$