Question

How do you evaluate the integral `int dx/(x^(19/20))` from 0 to 5 if it converges?

Answer 1

`20root(20)5`

Explanation:

`int_0^5dx/x^(19/20)`

Take the limit as `xrarr0`, since `1/x^(19/20)` is undefined for `x=0`.

`=lim_(brarr0)int_b^5x^(-19/20)dx`

`=lim_(brarr0)[20x^(1/20)]_b^5`

`=lim_(brarr0)(20(5)^(1/20)-20(b)^(1/20))`

Note that `20(0)^(1/20)=0`:

`=20(5)^(1/20)`

`=20root(20)5`