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Question

The area bounded athe curves y=ex,y=e-x and the straight line x=1 is given by


A

e+e-1ā€“2

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B

e-e-1

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C

e+e-1

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D

e+e-1+2

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Solution

The correct option is A

e+e-1ā€“2


Explanation for the correct option:

Step:1 Finding coordinates of point A and B

Two curves are y=ex,y=e-x

Now, for finding the point of intersection of ex and e-x

ex=e-xā‡’x=0ā‡’y=e0ā‡’y=1

Therefore, the two curves meet at A0,1

Now, for finding the point of intersection of ex and x=1

y=ex=e1=e

Therefore, the two curves meet at B1,e.

Step:2 Finding coordinates of point B

ow, for finding the point of intersection of e-x and x=1

y=e-x=e-1

Therefore, the two curves meet at C1,e-1

For x>0,ex>e-x

the area bounded is

Step:3 Finding Integral Area

A=āˆ«01ex-e-xdx=ex+e-x01=(e+e-1)āˆ’(e0+e-0)=e+1e-(1+1)=e+e-1-2

Hence, the correct answer is option A.


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