Browse Questions

# Integrate $I= \int \limits_0^1 e^{x^2} dx$

$\begin {array} {1 1} (a)\;I \in (0,1) \\ (b)\;I \in (e, \infty) \\ (c)\;I \in (1,e) \\ (d)\;I \in (1,\infty) \end {array}$

To solve this type of one, which Integration is not possible, find $max ^m, min ^m$ value of its $f/n$ :
$\int \limits_a^b f(x) => m- min, M-max$
$m^c (b-a) < \int \limits_a^b f (x) dx < M [b-a]$
for its $minz =1$
$max ^n=e$
$1. (1-0) < \int \limits _0^1 e^{x^2}.dx < e[1-0]$
$\int \limits _0^1 e^{x^2}.dx \in (1,e)$
Hence c is the correct answer.