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人気のある微分積分 >

integral from 4 to 5 of x/(4-x^2)

解

\int_{4}^{5} \frac{x}{4 - x ^{2}} d x

解

\frac{1}{2} ln (\frac{4}{7})

+1

十進法表記

- 0.27980 \dots

解答ステップ

\int_{4}^{5} \frac{x}{4 - x ^{2}} d x

u置換積分法を適用する

= \int_{- 12}^{- 21} - \frac{1}{2 u} d u

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

= - \int_{- 21}^{- 12} - \frac{1}{2 u} d u

定数を除く:

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

= - (- \frac{1}{2} \cdot \int_{- 21}^{- 12} \frac{1}{u} d u)

共通積分を使用する:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - (- \frac{1}{2} [ln ∣ u ∣]_{- 21}^{- 12})

簡素化

= \frac{1}{2} [ln ∣ u ∣]_{- 21}^{- 12}

限度を計算する:

ln (12) - ln (21)

= \frac{1}{2} (ln (12) - ln (21))

簡素化

= \frac{1}{2} ln (\frac{4}{7})

グラフ

人気の例

integral from 0 to 1 of (9x)/((2x+1)^3)

\int_{0}^{1} \frac{9 x}{( 2 x + 1 ) ^{3}} d x

integral from 0 to infinity of |x^2-1|

\int_{0}^{\infty} x^{2} - 1 d x

integral from 1 to 2 of (sin(ln(x)))/x

\int_{1}^{2} \frac{sin ( ln ( x ) )}{x} d x

integral from 0 to 4 of x/(sqrt(x^2+4))

\int_{0}^{4} \frac{x}{x ^{2} + 4} d x

integral from x^2 to 4 of sqrt(y)cos(y)

\int_{x^{2}}^{4} y cos (y) d y