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人気のある微分積分 >

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

解

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

解

\frac{4}{3}

+1

十進法表記

1.33333 \dots

解答ステップ

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

定数を除く:

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

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

拡張

(x - 2)^{2} : x^{2} - 4 x + 4

= \frac{1}{2} \cdot \int_{0}^{2} x^{2} - 4 x + 4 d x

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}{2} (\int_{0}^{2} x^{2} d x - \int_{0}^{2} 4 x d x + \int_{0}^{2} 4 d x)

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} 4 x d x = 8

\int_{0}^{2} 4 d x = 8

= \frac{1}{2} (\frac{8}{3} - 8 + 8)

簡素化

\frac{1}{2} (\frac{8}{3} - 8 + 8) : \frac{4}{3}

= \frac{4}{3}

グラフ

人気の例

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

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

integral from 0 to 1 of (x^2)/(1+y^2)

\int_{0}^{1} \frac{x ^{2}}{1 + y ^{2}} d y

integral from 0 to 4 of (2x+5)(3x-1)

\int_{0}^{4} (2 x + 5) (3 x - 1) d x

integral from 0 to 8 of x^{7/3}

\int_{0}^{8} x^{\frac{7}{3}} d x

integral from 1 to 2 of x^{ln(x)}

\int_{1}^{2} x^{l n (x)} d x