The integral of the function \( \frac{1}{x^n} \) from 0 to \( a \) (where \( a > 0 \)) converges or diverges based on the value of \( n \). Specifically, the integral converges if \( n < 1 \) and diverges if \( n \geq 1 \). This conclusion is derived from evaluating the improper integral \( \int_0^a x^{-n} dx \) using limits, which is essential for handling the behavior near the lower limit of integration.
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dami said:Homework Statement
give a general rule for when Integral (1/x^n) from (x, 0, a), a>0 converges or diverges.
Homework Equations
The Attempt at a Solution
I have checked the textbooks for this answer but i can't seem to find it. The closest i got was Integral (1/x^n) from (x, 1, infinity), converges or diverges.