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人気のある微分積分 >

integral from 0 to 4 of tsqrt(16-3t)

解

\int_{0}^{4} t 16 - 3 t d t

解

\frac{3008}{135}

+1

十進法表記

22.28148 \dots

解答ステップ

\int_{0}^{4} t 16 - 3 t d t

u置換積分法を適用する

= \int_{16}^{4} \frac{u ( u - 16 )}{9} d u

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

= - \int_{4}^{16} \frac{u ( u - 16 )}{9} d u

定数を除く:

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

= - \frac{1}{9} \cdot \int_{4}^{16} u (u - 16) d u

拡張

u (u - 16) : u^{\frac{3}{2}} - 16 u

= - \frac{1}{9} \cdot \int_{4}^{16} u^{\frac{3}{2}} - 16 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}{9} (\int_{4}^{16} u^{\frac{3}{2}} d u - \int_{4}^{16} 16 u d u)

\int_{4}^{16} u^{\frac{3}{2}} d u = \frac{1984}{5}

\int_{4}^{16} 16 u d u = \frac{1792}{3}

= - \frac{1}{9} (\frac{1984}{5} - \frac{1792}{3})

簡素化

- \frac{1}{9} (\frac{1984}{5} - \frac{1792}{3}) : \frac{3008}{135}

= \frac{3008}{135}

グラフ

人気の例

integral of 3x^24x^4

\int 3 x^{2} 4 x^{4} d x

limit as x approaches 0 of 4-5x

x \to 0 lim (4 - 5 x)

derivative f(x)=x^2-5,c=3

d er i v a t i v e f (x) = x^{2} - 5, c = 3

integral from-2 to 3 of (24)/(x^4)

\int_{- 2}^{3} \frac{24}{x ^{4}} d x

xy^'-3y^2=0,y(e)=1

x y^{^{'}} - 3 y^{2} = 0, y (e) = 1