\(\rm \int_{1}^{\infty} \frac{4}{x^4}dx\) విలువ ఎంత?

Question

Question

Answer 1

పద్ధతి:

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

సాధన:

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

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

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

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

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

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

= \(\frac 4 3\)