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Math Help - area with minimum and maximum

  1. #1
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    area with minimum and maximum

    If \mathbb{S} be The Area of The Region enclosed by y=e^{-x^2}\;,x=0\;,y=0\;,x=1. Then


    Which one is Right


    options:


    \displaystyle (a)\;\;\mathbb{S}\geq \frac{1}{e}


    \displaystyle (b)\;\;\mathbb{S}\geq 1-\frac{1}{e}


    \displaystyle (c)\;\;\mathbb{S}\leq \frac{1}{4}\left(1+\frac{1}{\sqrt{e}}\right)


    \displaystyle (d)\;\;\mathbb{S}\leq \frac{1}{\sqrt{2}}+\frac{1}{\sqrt{e}}\left(1-\frac{1}{\sqrt{2}}\right)
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  2. #2
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    Re: area with minimum and maximum

    I have Tried for lower bond

    like \displaystyle \int_{0}^{1}e^{-x^2}dx\geq \int_{0}^{1}e^{-x}dx=(1-\frac{1}{e})

    So I am getting (ii) option

    How can I calculate for Upper Bond
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