Evaluate the ff, improper integrals.

${\int}_{1}^{\mathrm{\infty}}\frac{1}{{x}^{3}}dx$

glamrockqueen7
2021-05-29
Answered

Evaluate the ff, improper integrals.

${\int}_{1}^{\mathrm{\infty}}\frac{1}{{x}^{3}}dx$

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cheekabooy

Answered 2021-05-30
Author has **83** answers

Step 1

The objective is to evaluate the given improper integrals:

${\int}_{1}^{\mathrm{\infty}}\frac{1}{{x}^{3}}dx$

Step 2

Evaluate the given integral as:

${\int}_{1}^{\mathrm{\infty}}\frac{1}{{x}^{3}}dx=[\int \frac{1}{{x}^{3}}dx{]}_{1}^{\mathrm{\infty}}$

$=[\frac{{x}^{-3+1}}{-3+1}{]}_{1}^{\mathrm{\infty}}=[\frac{1}{-2{x}^{2}}{]}_{1}^{\mathrm{\infty}}=[0+\frac{1}{2\times {1}^{2}}]$

$=\frac{1}{2}$

Thus,

${\int}_{1}^{\mathrm{\infty}}\frac{1}{{x}^{3}}dx=\frac{1}{2}$

The objective is to evaluate the given improper integrals:

Step 2

Evaluate the given integral as:

Thus,

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