ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

integral from 0 to 2/9 of 1/(81x^2+4)

解

\int_{0}^{\frac{2}{9}} \frac{1}{81 x ^{2} + 4} d x

解

\frac{π}{72}

+1

十進法表記

0.04363 \dots

解答ステップ

\int_{0}^{\frac{2}{9}} \frac{1}{81 x ^{2} + 4} d x

置換積分法を適用する

= \int_{0}^{1} \frac{1}{18 ( u ^{2} + 1 )} d u

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{18} \cdot \int_{0}^{1} \frac{1}{u ^{2} + 1} d u

共通積分を使用する:

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= \frac{1}{18} [arctan (u)]_{0}^{1}

限度を計算する:

\frac{π}{4}

= \frac{1}{18} \cdot \frac{π}{4}

簡素化

= \frac{π}{72}

グラフ

人気の例

integral from 0 to x of cos^2(x)

\int_{0}^{x} cos^{2} (x) d x

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

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

integral from 0 to infinity of t^2e^{-t}

\int_{0}^{\infty} t^{2} e^{- t} d t

integral from 0 to 4 of xcos((npix)/4)

\int_{0}^{4} x cos (\frac{nπ x}{4}) d x

integral from-1 to 4 of x^2+2x-4

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