Question #07106

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Answer 1 · 2017-11-07T02:47:47

$3/(root(3)(5)]$

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:

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