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Question

Let f be a real valued function satisfying f(xy)=f(x)f(y) and ltx0f(1+x)x=3. Then find the area bounded by the curve y=f(x), the y-axis and the line y=3 in sq units


A
e3
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B
3e
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C
e+3
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D
3e
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Solution

The correct option is C 3e
f(xy)=f(x)f(y)
x=y=1f(1)=0
f1(x)=lth0f(x+h)f(x)h
=ltx0f(1+hx)h=3x
f(x)=3logx
area =3xdy
=3ey3dy=3e

Mathematics

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