The value of the integral `int_(0)^(1) e^(x^(2))dx` lies in the integral

Options

A. (0,1)
B. (-1,0)
C. (1, e)
D. none of these

Answer

C

Explanation

Since `e^(x^(2))` is an increasing function on (0,1).
`:. M=e^(0)=1 " and "M=e^(1)=e`, where
m and M are minimum and maximum values of f(x)`=e^(x^(2))` in the integral (0,1) for all `x in (0,1)`
`rArr 1(1-0) lt overset(1)underset(0)int e^(x^(2))dx lt e(1-0) rArr1 lt overset(1)underset(0)int e^(x^(2))dx lt e`.