Question

Evaluate the ff, improper integrals. \int_{1}^{\infty}\frac{1}{x^{3}}dx

Applications of integrals
ANSWERED
asked 2021-05-29
Evaluate the ff, improper integrals.
\(\int_{1}^{\infty}\frac{1}{x^{3}}dx\)

Expert Answers (1)

2021-05-30
Step 1
The objective is to evaluate the given improper integrals:
\(\int_{1}^{\infty}\frac{1}{x^{3}}dx\)
Step 2
Evaluate the given integral as:
\(\int_{1}^{\infty}\frac{1}{x^{3}}dx=[\int\frac{1}{x^{3}}dx]_{1}^{\infty}\)
\(=[\frac{x^{-3+1}}{-3+1}]_{1}^{\infty}=[\frac{1}{-2x^{2}}]_{1}^{\infty}=[0+\frac{1}{2\times 1^{2}}]\)
\(=\frac{1}{2}\)
Thus,
\(\int_{1}^{\infty}\frac{1}{x^{3}}dx=\frac{1}{2}\)
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