Log integration ~ (1 Viewer)

[Juliaan]

Evaluate:

/4
|
| [( x^2 - 1) / x] dx
|
/2

Please and ty.

 

[whackymac]

Divide the numerator individually,
ie. (x^2 - 1) / x = x - (1 / x)

Now integrate that instead,
/4
|
| x - (1/x) dx = [ (x^2)/2 - ln x ] -> then sub in the borders for your answer.
|
/2

 

[LoneWolf1990]

/4
|
| [( x^2 - 1) / x] dx
|
/2

=

/4
|
| [x - 1 / x] dx
|
/2

=
4
[x^2/2-lnx]
2
=

(8-ln(4))-(2-ln(2))

=6-ln(4)+ln(2)

 

[Juliaan]

Thanks heaps guys ~