Question

Question #07106

Answer 1

`3/(root(3)(5)]`

Explanation:

The first step is to solve the integral:

`int1/x^(4/3)dx` really is `int` `x^-(4/3)dx`

`int` `x^-(4/3)dx ->-3/(root(3)(x))+"c"`

Knowing this we can proceed:

`int_5^oo 1/x^(4/3) dx` is equal to what is below

`lim_{b to oo}-3/(root(3)(x))` Evaluated from `5` to `b`

`lim_{b to oo}[-3/(root(3)(b))-(-3/(root(3)(5)))]`

`lim_{b to oo}[-3/(root(3)(b))+3/(root(3)(5))]`

When we take the limit of:

`lim_{b to oo}[-3/(root(3)(b))]` We get `-3/oo` Anything over infinite is zero.

`[-3/(root(3)(oo))+3/(root(3)(5))]`

The answer should look like this once you take the limit of course you can disregard the zero:

`[0+3/(root(3)(5))]`