Definite Integral for $\int_{0}^{a} x^{−n}dx$

Asked Nov 12 '20 at 05:47

Active Nov 12 '20 at 06:04

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Definite Integral for $\int_{0}^{a} x^{−n}dx$ where $n<=0$ and $0 < x < a$

$\int x^{−n}dx = x^{(-n + 1)}/(-n + 1)$. I'm not able to plug in the lower limit $0$ here because won't the result reaches $\infty$? I'm sure something is wrong with the thinking. If anyone can clarify it would be great.

edited Nov 12 '20 at 06:04

asked Nov 12 '20 at 05:47

SrikRaja

1

If $n \leq 0$ the $-n+1>0$. So how do you get $\infty$? – Kavi Rama Murthy Nov 12 '20 at 05:52
It is strange to use both $-n$ and $n \leq 0$. Together these imply that you are integrating a nonnegative power of $x$ (regardless of which variable is the variable of integration). – Eric Towers Nov 12 '20 at 05:55
@Kavi Rama Murthy, thanks. I overlooked that point. Now, I get $ x^{(-n + 1)} is 0 $ as x approaches 0 – SrikRaja Nov 12 '20 at 06:07
@EricTowers, I have corrected the question – SrikRaja Nov 12 '20 at 06:25

Definite Integral for $\int_{0}^{a} x^{−n}dx$

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