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人気のある微分積分 >

integral from 3 to 4 of 1/(4-x^2)

解

\int_{3}^{4} \frac{1}{4 - x ^{2}} d x

解

\frac{ln ( 3 ) - ln ( 5 )}{4}

+1

十進法表記

- 0.12770 \dots

解答ステップ

\int_{3}^{4} \frac{1}{4 - x ^{2}} d x

置換積分法を適用する

= \int_{\frac{3}{2}}^{2} \frac{1}{2 ( - u ^{2} + 1 )} 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_{\frac{3}{2}}^{2} \frac{1}{- u ^{2} + 1} d u

共通積分を使用する:

\int \frac{1}{- u ^{2} + 1} d u = \frac{ln ∣ u + 1 ∣}{2} - \frac{ln ∣ u - 1 ∣}{2}

= \frac{1}{2} [\frac{ln ∣ u + 1 ∣}{2} - \frac{ln ∣ u - 1 ∣}{2}]_{\frac{3}{2}}^{2}

簡素化

\frac{1}{2} [\frac{ln ∣ u + 1 ∣}{2} - \frac{ln ∣ u - 1 ∣}{2}]_{\frac{3}{2}}^{2} : \frac{1}{2} [\frac{ln ∣ u + 1 ∣ - ln ∣ u - 1 ∣}{2}]_{\frac{3}{2}}^{2}

= \frac{1}{2} [\frac{ln ∣ u + 1 ∣ - ln ∣ u - 1 ∣}{2}]_{\frac{3}{2}}^{2}

限度を計算する:

\frac{ln ( 3 ) - ln ( \frac{5}{2} ) - ln ( 2 )}{2}

= \frac{1}{2} \cdot \frac{ln ( 3 ) - ln ( \frac{5}{2} ) - ln ( 2 )}{2}

簡素化

= \frac{ln ( 3 ) - ln ( 5 )}{4}

グラフ

人気の例

integral from-4 to 5 of (|3x^2-12|+x^3)

\int_{- 4}^{5} (3 x^{2} - 12 + x^{3}) d x

integral from 4 to 5 of 4/(x^2-1)

\int_{4}^{5} \frac{4}{x ^{2} - 1} d x

integral from 0 to 2pi of cos^2(t)sin(t)

\int_{0}^{2 π} cos^{2} (t) sin (t) d t

integral from 1-y to-y^2+y+1 of 2y

\int_{1 - y}^{- y^{2} + y + 1} 2 y d y

integral from 0 to t of e^{-t+x}cos(x)

\int_{0}^{t} e^{- t + x} cos (x) d x