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 1 of sqrt(1-r^2)*r

解

\int_{0}^{1} 1 - r^{2} \cdot r d r

解

\frac{1}{3}

+1

十進法表記

0.33333 \dots

解答ステップ

\int_{0}^{1} 1 - r^{2} r d r

u置換積分法を適用する

= \int_{1}^{0} - u^{2} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{1} - u^{2} d u

定数を除く:

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

= - (- \int_{0}^{1} u^{2} d u)

べき乗則を適用する

= - (- [\frac{u ^{3}}{3}]_{0}^{1})

簡素化

= [\frac{u ^{3}}{3}]_{0}^{1}

限度を計算する:

\frac{1}{3}

= \frac{1}{3}

グラフ

人気の例

integral from-1 to 1 of |5x-3|

\int_{- 1}^{1} ∣ 5 x - 3 ∣ d x

integral from pi/6 to pi/2 of 6sin(x)

\int_{\frac{π}{6}}^{\frac{π}{2}} 6 sin (x) d x

integral from 0 to pi/(12) of xtan^2(4x)

\int_{0}^{\frac{π}{12}} x tan^{2} (4 x) d x

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

\int_{0}^{1} x (x^{2} - 1) d x

integral from 0 to 40 of x\sqrt[3]{675x}

\int_{0}^{40} x 3 675 x d x