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人気のある微分積分 >

integral from 0 to 3 of x/(sqrt(16+3x))

解

\int_{0}^{3} \frac{x}{16 + 3 x} d x

解

\frac{26}{27}

+1

十進法表記

0.96296 \dots

解答ステップ

\int_{0}^{3} \frac{x}{16 + 3 x} d x

u置換積分法を適用する

= \int_{4}^{5} \frac{2 ( u ^{2} - 16 )}{9} d u

定数を除く:

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

= \frac{2}{9} \cdot \int_{4}^{5} u^{2} - 16 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{2}{9} (\int_{4}^{5} u^{2} d u - \int_{4}^{5} 16 d u)

\int_{4}^{5} u^{2} d u = \frac{61}{3}

\int_{4}^{5} 16 d u = 16

= \frac{2}{9} (\frac{61}{3} - 16)

簡素化

\frac{2}{9} (\frac{61}{3} - 16) : \frac{26}{27}

= \frac{26}{27}

グラフ

人気の例

integral from 0 to x of sqrt(x^4+x^6)

\int_{0}^{x} x^{4} + x^{6} d x

integral from 0 to 1 of x^3+sqrt(x)

\int_{0}^{1} x^{3} + x d x

integral from 0 to arctan(3) of sin(2x)

\int_{0}^{a r c t a n (3)} sin (2 x) d x

integral from 0 to infinity of 3/(x+5)

\int_{0}^{\infty} \frac{3}{x + 5} d x

integral from-4 to 4 of-e^{1/4 x}

\int_{- 4}^{4} - e^{\frac{1}{4} x} d x