Area of the region bounded by y = ex , y = e-x , x = 0 and x = 1 in sq. units is

Question

Area of the region bounded by y = ex , y = e-x , x = 0 and x = 1 in sq. units is (A) ( e + (1/e))2 (B) ( e - (1/e))2 (C) ( √e + (1/√e) )2 (D) ( √e - (1/√e) )2

Tardigrade Admin · Accepted Answer

y = e x , y = e - x Then, area bounded by these two curves s given by A =∫01( e x - e - x ) d x =∫01 e x d x -∫01 e - x dx =( e 1- 1 )+ 1 ( e -1- 1 ) = e + e - 1 - 2 =(√ e -(1/√ e ))2 sq units.

Q. Area of the region bounded by $y = e^{x}, y = e^{- x}, x = 0$ and $x = 1$ in sq. units is

$(e + \frac{1}{e})^{2}$

$(e - \frac{1}{e})^{2}$

$(e + \frac{1}{e})^{2}$

$(e - \frac{1}{e})^{2}$

$y = e^{x}, y = e^{- x}$
Then, area bounded by these two curves s given by $A = \int_{0}^{1} (e^{x} - e^{- x}) d x = \int_{0}^{1} e^{x} d x - \int_{0}^{1} e^{- x} d x$
$= (e^{1} - 1) + 1 (e^{- 1} - 1)$
$= e + e^{- 1} - 2$
$= (e - \frac{1}{e})^{2}$ sq units.

Q. Area of the region bounded by y=ex,y=e−x,x=0 and x=1 in sq. units is

(e+e1​)2

(e−e1​)2

(e​+e​1​)2

(e​−e​1​)2

y=ex,y=e−x Then, area bounded by these two curves s given by A=∫01​(ex−e−x)dx=∫01​exdx−∫01​e−xdx =(e1−1)+1(e−1−1) =e+e−1−2 =(e​−e​1​)2 sq units.

Q. Area of the region bounded by $y = e^{x}, y = e^{- x}, x = 0$ and $x = 1$ in sq. units is

$(e + \frac{1}{e})^{2}$

$(e - \frac{1}{e})^{2}$

$(e + \frac{1}{e})^{2}$

$(e - \frac{1}{e})^{2}$

$y = e^{x}, y = e^{- x}$
Then, area bounded by these two curves s given by $A = \int_{0}^{1} (e^{x} - e^{- x}) d x = \int_{0}^{1} e^{x} d x - \int_{0}^{1} e^{- x} d x$
$= (e^{1} - 1) + 1 (e^{- 1} - 1)$
$= e + e^{- 1} - 2$
$= (e - \frac{1}{e})^{2}$ sq units.