A calculus problem by Kïñshük Sïñgh

Calculus Level 4

$\int _{ \infty }^{ 0 }{ \frac { x{ e }^{ -x } }{ \sqrt { 1-{ e }^{ -2x } } } } \, dx = \, ?$

Clarification : The lower limit is indeed $\infty$ , and not $-\infty$ .

3

\frac { -\pi }{ 2 } \ln { 2 }

\frac { \pi }{ 2 } \ln { 2 }

0

2 solutions

Ayush Sharma
Jun 19, 2017

Hope you all understand this

Raj Rajput
Apr 22, 2015

easy but a tricky one

put e to power -x to sina then proceed

it will become integration 0 to pi/2 logsina da then we now the rest apply properties same question that of ncert miscellaneous .... :)

Maybe you should change the answers...

F(x) is, on this interval, always smaller than zero so the integral must be negative and you have 3 positive but one negative answer.

Вук Радовић - 5 years, 8 months ago

With a lower limit of $-\infty$ how does this integral come out to a real value at all? The function doesn't take any real values on that interval.

First Last - 3 years, 12 months ago

The answer seems like it is selected from using the limits in the problem without the clarification.

First Last - 3 years, 12 months ago