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人気のある微分積分 >

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

解

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

解

\frac{π}{4}

+1

十進法表記

0.78539 \dots

解答ステップ

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

不定積分を計算する:

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

限度を計算する:

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

= 0 - (- \frac{π}{4})

簡素化

= \frac{π}{4}

人気の例

integral from 0 to 7 of 1/(x^2+49)

\int_{0}^{7} \frac{1}{x ^{2} + 49} d x

integral from 1 to 2 of (8x^7-3x^2+2x)

\int_{1}^{2} (8 x^{7} - 3 x^{2} + 2 x) d x

integral from 0 to x of sin(u)

\int_{0}^{x} sin (u) d u

integral from 0 to 1 of 1/(sqrt(81-x^2))

\int_{0}^{1} \frac{1}{81 - x ^{2}} d x

integral from 0 to 2 of x/(sqrt(5+x^2))

\int_{0}^{2} \frac{x}{5 + x ^{2}} d x