What is the integral from-infinity to 0 of 1/(x^2+4) ?

The integral from-infinity to 0 of 1/(x^2+4) is pi/4

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integral from-infinity to 0 of 1/(x^2+4)

\int_{- \infty}^{0} \frac{1}{x ^{2} + 4} d x

\frac{π}{4}

Decimal

0.78539 \dots

Solution steps

\int_{- \infty}^{0} \frac{1}{x ^{2} + 4} d x

Compute the indefinite integral:

\int \frac{1}{x ^{2} + 4} d x = \frac{1}{2} arctan (\frac{x}{2}) + C

Compute the boundaries:

\int_{- \infty}^{0} \frac{1}{x ^{2} + 4} d x = 0 - (- \frac{π}{4})

= 0 - (- \frac{π}{4})

Simplify

= \frac{π}{4}

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What is the integral from-infinity to 0 of 1/(x^2+4) ?
The integral from-infinity to 0 of 1/(x^2+4) is pi/4