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Definition of Relations

Let S be the ...

Question

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

A

S < 1 - \frac{1}{e}

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B

S > 1 - \frac{1}{e}

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C

S = 1 - \frac{1}{e}

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D

S = 1

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Solution

The correct option is B $S > 1 - \frac{1}{e}$
$S = \int_{0}^{1} e^{- x^{2}} d x \geq \int_{0}^{1} e^{- x} d x = 1 - \frac{1}{e}$

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Similar questions

S

be the area of the region enclosed by

y = e^{- x^{2}}, y = 0, x = 0

x = 1

Let $S$ be the area bounded by $y = e^{| cos 4 x |}, x = 0, y = 0$ and $x = π$ , Then

\begin{matrix} L i s t I & L i s t I I P . & A r e a b o u n d e d b y y = x | x |, x - a x i s, & 1. & \frac{10}{3} x = 1 a n d x = - 1 Q . & A r e a b o u n d e d b y x - y + 2, & 2. & \frac{64}{3} x = \sqrt{y} a n d x = 0 R . & A r e a e n c l o s e d b y y^{2} = x & 3. & \frac{2}{3} a n d y = | x | S . & A r e a b o u n d e d b y y^{2} = x & 4. & \frac{1}{6} y = 4 a n d x = 0 \end{matrix}

S

be the circle in the

x y

-plane defined by the equation

x^{2} + y^{2} = 4

E_{1} E_{2}

F_{1} F_{2}

be the chords of

S

passing through the point

P_{0} (1, 1)

and parallel to the

x

y

-axis, respectively. Let

G_{1} G_{2}

be the chord of

S

passing through

P_{0}

and having slope

- 1

. Let the tangents to

S

E_{1}

E_{2}

E_{3}

, the tangents to

S

F_{1}

F_{2}

F_{3}

, and the tangents to

S

G_{1}

G_{2}

G_{3}

. Then, the points

E_{3}, F_{3}

G_{3}

lie on the curve

S = {(x, y) \in R^{2} : \frac{y^{2}}{1 + r} - \frac{x^{2}}{1 - r} = 1}

r \neq \pm 1

S

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