JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

A function

f(x)

satisfies

f(x)=f\left(\frac{c}{x}\right)

for some real number

c(c>1)

and

\forall \, x>0

. If

\int\limits_{1}^{\sqrt{c}} \frac{f(x)}{x} d x=3

, then the value of

\int\limits_{1}^c \frac{f(x)}{x} d x

View answer and explanation

Correct option: A

Option A (6) is correct because by using the substitution

u = \frac{c}{x}

and the given property of the function, the integral from

\sqrt{c}

c

is equal to the integral from 1 to

\sqrt{c}

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