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Q.

Let S be the area of the region enclosed by ${y = e}^{{-x}^{2}}, y = 0, x = 0$ and $x = 1$ . Then

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a

$S \geq 1 - \frac{1}{e}$

b

$S \geq \frac{1}{e}$

c

$S \leq \frac{1}{4} (1 + \frac{1}{\sqrt{e}})$

d

$S \leq \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{e}} (1 - \frac{1}{\sqrt{2}})$

answer is A, B, D.

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Detailed Solution

$\frac{1}{e} \leq S \leq 1 - \frac{1}{e}; S \leq \int_{0}^{1/ \sqrt{2}} e^{- x^{2}} d x + \int_{1 / \sqrt{2}}^{1} e^{- x^{2}} d x$

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