# For each of the following improper integrals, note Why it

For each of the following improper integrals, note Why it is omproper, and then set up the limit(s) that would be used to evaluate the integral.
${\int }_{1}^{\mathrm{\infty }}\frac{1}{{x}^{3}}dx$
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${\int }_{1}^{\mathrm{\infty }}\frac{1}{{x}^{3}}dx$
For the given integration the upper limit is infinity also the integrand of the limit goes to infinity in the range of given integration at point x = 0.
Therefore, the given integral is improper.
Now to set up the given integral:
${\int }_{1}^{\mathrm{\infty }}\frac{1}{{x}^{3}}dx=\underset{t\to \mathrm{\infty }}{lim}{\int }_{1}^{t}\frac{1}{{x}^{3}}dx$