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 x^2sqrt(6x+9)

解

\int_{0}^{1} x^{2} 6 x + 9 d x

解

\frac{25 15 - 54}{35}

+1

十進法表記

1.22355 \dots

解答ステップ

\int_{0}^{1} x^{2} 6 x + 9 d x

u置換積分法を適用する

= \int_{9}^{15} \frac{u ( u - 9 ) ^{2}}{216} d u

定数を除く:

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

= \frac{1}{216} \cdot \int_{9}^{15} u (u - 9)^{2} d u

拡張

u (u - 9)^{2} : u^{\frac{5}{2}} - 18 u^{\frac{3}{2}} + 81 u

= \frac{1}{216} \cdot \int_{9}^{15} u^{\frac{5}{2}} - 18 u^{\frac{3}{2}} + 81 u d u

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{216} (\int_{9}^{15} u^{\frac{5}{2}} d u - \int_{9}^{15} 18 u^{\frac{3}{2}} d u + \int_{9}^{15} 81 u d u)

\int_{9}^{15} u^{\frac{5}{2}} d u = \frac{6750 15 - 4374}{7}

\int_{9}^{15} 18 u^{\frac{3}{2}} d u = 18 (9015 - \frac{486}{5})

\int_{9}^{15} 81 u d u = 81 (1015 - 18)

= \frac{1}{216} (\frac{6750 15 - 4374}{7} - 18 (9015 - \frac{486}{5}) + 81 (1015 - 18))

簡素化

\frac{1}{216} (\frac{6750 15 - 4374}{7} - 18 (9015 - \frac{486}{5}) + 81 (1015 - 18)) : \frac{25 15 - 54}{35}

= \frac{25 15 - 54}{35}

グラフ

人気の例

integral from 0 to 80 of (1-t/(80))^a

\int_{0}^{80} (1 - \frac{t}{80})^{a} d t

integral from 0 to 2pi of (1+cos(2θ))/2

\int_{0}^{2 π} \frac{1 + cos ( 2 θ )}{2} d θ

integral from-1 to 1 of x(5-x)^2

\int_{- 1}^{1} x (5 - x)^{2} d x

integral from 1 to 5 of x/(sqrt(2x-3))

\int_{1}^{5} \frac{x}{2 x - 3} d x

integral from 1 to 3 of 3e^{x+6}

\int_{1}^{3} 3 e^{x + 6} d x