Questions: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If it diverges to infinity, state your answer as "oo" (without the quotation marks). If it diverges to negative infinity, state your answer as "-00". If it diverges without being infinity or negative infinity, state your answer as "DNE". [ int-infty^infty(-4 x^4) d x ]

Solution Steps

We need to evaluate the integral

\[ \int_{-\infty}^{\infty} \left(-4 x^{4}\right) dx. \]

To analyze the convergence, we split the integral into two parts:

\[ \int_{-\infty}^{0} \left(-4 x^{4}\right) dx + \int_{0}^{\infty} \left(-4 x^{4}\right) dx. \]

1. For the first integral:

\[ \int_{-\infty}^{0} \left(-4 x^{4}\right) dx = -\infty. \]

2. For the second integral:

\[ \int_{0}^{\infty} \left(-4 x^{4}\right) dx = -\infty. \]

Since both integrals diverge to negative infinity, the overall integral diverges.

Final Answer