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The area enclosed between the curve y = ...

The area enclosed between the curve `y = log_e (x +e )` and the coordinate axes is

A

4

B

3

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
D
The area enclosed by `y=log_(e)(x+e)` and the coorcinate axes is shaded in Fig. 17.

Let A be the required area. Then,
`A=underset(1-e)overset(0)(int)y dx=underset(1-e)overset(0)(int)log_(e)(x+e)dx`
`impliesA=[xlog_(e)(x+e)]_(1-e)^(0)-underset(1-e)overset(0)(int)(x)/(x+e)dx`
`impliesA=[xlog _(e)(x+e)]_(1-e)^(0)-[x-elog_(e)(x+e)]_(1-e)^(0)`
`impliesA=0-[(0-e)-(1-e)+0]=1` sq. units
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