Question

Find the point of intersection of the curves y=ln(x+2) and y=2+ln(2-x)

Answer 1

Answer:

Correct option is

C

3−e

Given curves, y=lnx & y=(lnx)

2

Points of intersection of given curves are, (1,0) and (e,1)

Hence required area is,

A=∫

1

e

(lnx−(lnx)

2

)dx

On solving it by parts we get

A=[xlnx−x]

1

e

−[x(lnx)

2

−∫

1

e

2lnxdx]

A=[xlnx−x]

1

e

−[x(lnx)

2

−2xlnx+2x]

1

e

A=[xlnx−x−x(lnx)

2

+2xlnx−2x]

1

e

A=∣3x(lnx−1)∣

1

e

−∣x(lnx)

2

∣

1

e

=3−e

Step-by-step explanation:

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