Question

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

Answer 1

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.