Home
Class 12
MATHS
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`
Promotional Banner

Similar Questions

Explore conceptually related problems

int_(a)^(b) f(x) dx =

int_(0)^(1)e^(2x)e^(e^(x) dx =)

Evaluate int_(0)^(1)(e^(-x)dx)/(1+e^(x))

The value of int_(0)^(oo) e^(-3x) x^(2) dx is

Let m,n be two positive real numbers and define f(n)=int_(0)^(oo)x^(n-1)e^(-x)dx and g(m,n)=int_(0)^(1)x^(m-1)(1-m)^(n-1)dx . It is known that f(n) for n gt 0 is finite and g(m, n) = g(n, m) for m, n gt 0. int_(0)^(oo)(x^(m-1))/((1+x)^(m+n))dx=

If a, b and c are real numbers, then the value of lim_(trarr0) ln((1)/(t)int_(0)^(t)(1+asinbx)^(c//x)dx) equals

Evaluate int(dx)/(sqrt(1+e^(x)+e^(2x)))

int(e^(x)+1)/(e^(x))dx :