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Calculus · Definite-Integrals

Integrate 1/(y^2 + 1) from 0 to oo

\int_{0}^{\infty} \frac{1}{y^{2} + 1}\, dy

Step by step

  1. \int_{0}^{\infty} \frac{1}{y^{2} + 1}\, dy

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

  2. \int \frac{1}{y^{2} + 1}\, dy = \operatorname{atan}{\left(y \right)}

    Recognise an inverse-trig / inverse-hyperbolic form.

  3. F(\infty) - F(0) = \left(\frac{\pi}{2}\right) - \left(0\right)

    Fundamental theorem of calculus: plug in the limits.

  4. = \frac{\pi}{2} \approx 1.5708

    Simplify.

Reveal the answer
\frac{\pi}{2}