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人気のある微分積分 >

面積 sqrt(x),x-6,x,2

解

面積

x, x - 6, x, 2

解

\frac{19}{6}

+1

十進法表記

3.16666 \dots

解答ステップ

交点を見つけるには以下を解く:

f_{i} (x) = f_{j} (x)

x = x - 6 : x = 9

x = x : x = 1, x = 0

x = 2 : x = 4

x - 6 = x :

解なし

x - 6 = 2 : x = 8

x = 2 : x = 2

= \int_{0}^{1} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{1}^{2} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{2}^{4} ∣ f_{1} (x) - f_{4} (x) ∣ d x + \int_{4}^{8} ∣ f_{1} (x) - f_{4} (x) ∣ d x + \int_{8}^{9} ∣ f_{2} (x) - f_{1} (x) ∣ d x

= \int_{0}^{1} x - x d x + \int_{1}^{2} x - x d x + \int_{2}^{4} x - 2 d x + \int_{4}^{8} x - 2 d x + \int_{8}^{9} x - 6 - x d x

\int_{0}^{1} x - x d x = \frac{1}{6}

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

\int_{2}^{4} x - 2 d x = - \frac{16 - 4 2}{3} + 4

\int_{4}^{8} x - 2 d x = \frac{32 2 - 16}{3} - 8

\int_{8}^{9} x - 6 - x d x = \frac{31}{2} - \frac{32 2}{3}

= \frac{1}{6} - \frac{4 2 - 2}{3} + \frac{3}{2} - \frac{16 - 4 2}{3} + 4 + \frac{32 2 - 16}{3} - 8 + \frac{31}{2} - \frac{32 2}{3}

簡素化

= \frac{19}{6}

グラフ

人気の例

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d er i v a t i v e x x^{2} + 1

derivative of (pi-x^2)

\frac{d}{d x} ((π - x)^{2})

integral of r^2((r^3)/9-8)^2

\int r^{2} (\frac{r ^{3}}{9} - 8)^{2} d r

f^'(x)=(3f(x))/(xln(x))

f^{^{'}} (x) = \frac{3 f ( x )}{x ln ( x )}

derivative of (14400/x)

\frac{d}{d x} (\frac{14400}{x})