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The area of the region enclosed by the c...

The area of the region enclosed by the curve `y=x, x=e,y=1/x` and the positive X-axis is

A

`(5)/(2)` square units

B

`(1)/(2)` square units

C

1 square units

D

`(3)/(2)` square units

Text Solution

Verified by Experts

The correct Answer is:
D

Required area = Area of `DeltaAOB` + Area of region ADCB
`=(1)/(2)xx1xx1+overset(e)underset(1)int(1)/(x)dx`
`=(1)/(2)+["In "x]_(1)^(e)`
`=(1)/(2)+1-0=(3)/(2)` sq. units
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