Express each of the following integrals as a $\Gamma$ function. By computer, evaluate numerically both the $\Gamma$ function and the original integral. $\int_{0}^{\infty} e^{-x^{4}} d x$ Hint: Put $x^{4}=u$
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Step 1
Substituting this into the integral, we get: $$\int_{0}^{\infty} e^{-x^{4}} d x = \int_{0}^{\infty} e^{-u} \frac{1}{4}u^{-\frac{3}{4}}du$$ Show more…
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