integrate the improper integral from 1 to infinity \frac{dx}{x^P} .Where the series converges

Question:

integrate the improper {eq}\int_{1}^{\infty} \frac{dx}{x^P}{/eq} .

Integration:

Given a function f of a real variable x and an interval (a, b) of the real line, the definite integral:

{eq}\int _a^{b \:}f\left(x\right)dx {/eq}

Answer and Explanation:

{eq}\int \frac{1}{x^P}dx=\int \:x^{-P}dx\\ \displaystyle=\frac{x^{-P+1}}{-P+1}\\ \displaystyle=0-\frac{1}{-P+1}\\ \displaystyle=\frac{1}{-P+1} {/eq}


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Integration Problems in Calculus: Solutions & Examples

from AP Calculus AB & BC: Homework Help Resource

Chapter 13 / Lesson 13
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