Evaluate the ff, improper integrals. \int_{1}^{\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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Expert Answer

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:
${\int }_{1}^{\mathrm{\infty }}\frac{1}{{x}^{3}}dx=\left[\int \frac{1}{{x}^{3}}dx{\right]}_{1}^{\mathrm{\infty }}$
$=\left[\frac{{x}^{-3+1}}{-3+1}{\right]}_{1}^{\mathrm{\infty }}=\left[\frac{1}{-2{x}^{2}}{\right]}_{1}^{\mathrm{\infty }}=\left[0+\frac{1}{2×{1}^{2}}\right]$
$=\frac{1}{2}$
Thus,
${\int }_{1}^{\mathrm{\infty }}\frac{1}{{x}^{3}}dx=\frac{1}{2}$
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