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Let a and b be two positive real numbers...

Let a and b be two positive real numbers. Then the value of `int_(a)^(b)(e^(x//a)-e^(b//x))/(x)dx` is

A

0

B

ab

C

1/ab

D

`e^(ab)`

Text Solution

Verified by Experts

The correct Answer is:
A
`I=int_(a)^(b)(e^(x//a)-e^(b//a))/(x)dx`
Put `(x)/(a)=(b)/(y)`
`rArr" "I=int_(b)^(a)(e^((b)/(y))-e^((y)/(a)))/((ab)/(y))(-(ab)/(y^(2)))dy`
`" "=int_(a)^(b)(b^(b//x)-e^(x//a))/(x)dx=-I`
`rArr" "2I=0`
`rArr" "I=0`
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