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Calculus · Definite-Integrals

Integrate e^(-x^2/4) from -oo to oo

\int_{-\infty}^{\infty} e^{- \frac{x^{2}}{4}}\, dx

Step by step

  1. \int_{-\infty}^{\infty} e^{- \frac{x^{2}}{4}}\, dx

    First find an antiderivative F, then evaluate F(b) − F(a).

  2. \int e^{- \frac{x^{2}}{4}}\, dx = \sqrt{\pi} \operatorname{erf}{\left(\frac{x}{2} \right)}

    Erf rule.

  3. F(\infty) - F(-\infty) = \left(\sqrt{\pi}\right) - \left(- \sqrt{\pi}\right)

    Fundamental theorem of calculus: plug in the limits.

  4. = 2 \sqrt{\pi} \approx 3.5449

    Simplify.

Reveal the answer
2 \sqrt{\pi}