The value of integral _0^1 e^ x^2 dx lies in interval - Vidyadip

MCQ

The value of integral $\int_0^1 {{e^{{x^2}}}} dx$ lies in interval

A
$(0,\,\,1)$
B
($ - 1,\,\,0)$
✓
$(1,\,\,e)$
D
None of these

✓

Answer

Correct option: C.

$(1,\,\,e)$

c
(c) For $0 < x < 1$, we have $1 < {e^{{x^2}}} < e$,

so that $\int_0^1 {1dx < \int_0^1 {{e^{{x^2}}}} dx < \int_0^1 {e\,dx} }$

${ \Rightarrow 1 < \int_0^1 {{e^{{x^2}}}dx < e.} } $

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