\(\rm \int_{1}^{\infty} \frac{4}{x^4}dx\) का मूल्यांकन कीजिए। 

  1. \(\frac 2 3\)
  2. \(\frac 4 3\)
  3. \(​​\frac 1 3\)
  4. उपरोक्त में से कोई नहीं 

Answer (Detailed Solution Below)

Option 2 : \(\frac 4 3\)
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संकल्पना:

\(\rm \int x^n dx = \frac{x^{n+1}}{n+1}+c\)

गणना:

I = \(\rm \int_{1}^{\infty} \frac{4}{x^4}dx\)

\(\rm \int_{1}^{\infty}4{x^{-4}}dx\)

\(\rm \left[\frac{4x^{-3}}{-3} \right ]_1^{\infty}\)

\(\rm \frac{-4}{3}\left[\frac{1}{x^3} \right ]_1^{\infty}\)

\(\rm \frac{-4}{3}\left[\frac{1}{\infty} - \frac{1}{1}\right ]\)

\(\rm \frac{-4}{3}[0-1]\)

\(\frac 4 3\)

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