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Determine whether the integral is convergent or divergent. ∫1[infinity]​x38​dx convergent divergent: If it is convergent, evaluate it

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To determine whether the integral
\displaystyle\sf \int_(1)^(\infty)x^(3/8)dx is convergent or divergent, we can use the p-test for improper integrals.

The p-test states that for the integral
\displaystyle\sf \int_(a)^(\infty)x^(p)dx, it converges if
\displaystyle\sf p>1, and it diverges if
\displaystyle\sf p\leq 1.

In our case,
\displaystyle\sf p=(3)/(8)<1. Therefore, the integral is divergent.

Since the integral is divergent, we do not need to evaluate it.

User Hugo Walter
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