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))]#