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Determine whether the integral is convergent or divergent. If it is convergent, then evaluate it....

Question:

Determine whether the integral is convergent or divergent. If it is convergent, then evaluate it.

{eq}\int_{0}^{\infty } x^2 e^{x^3}\, \mathrm{d}x {/eq}

Improper Integral: Substitution Rule:

This is an improper integral with the upper limit equal to infinity. It is equal to the limit of definite integrals from 0 to b when b diverges to infinity.

We calculate the definite integrals by using the substitution rule.

Answer and Explanation:

First we find the indefinite integral {eq}\displaystyle \; \int x^2 e^{x^3} \, \mathrm{d}x \; {/eq} , by using the substitution...

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