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人気のある微分積分 >

integral from 2 to 3 of (x-4)sqrt(5-x)

解

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

解

2 (3 + \frac{2 2 - 27 3}{15})

+1

十進法表記

- 2.39415 \dots

解答ステップ

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

u置換積分法を適用する

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

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

= - \int_{2}^{3} - 2 u^{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

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

拡張

u^{2} (- u^{2} + 1) : - u^{4} + u^{2}

= - (- 2 \cdot \int_{2}^{3} - u^{4} + u^{2} 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

= - (- 2 (- \int_{2}^{3} u^{4} d u + \int_{2}^{3} u^{2} d u))

\int_{2}^{3} u^{4} d u = \frac{9 3 - 4 2}{5}

\int_{2}^{3} u^{2} d u = 3 - \frac{2 2}{3}

= - (- 2 (- \frac{9 3 - 4 2}{5} + 3 - \frac{2 2}{3}))

簡素化

- (- 2 (- \frac{9 3 - 4 2}{5} + 3 - \frac{2 2}{3})) : 2 (3 + \frac{2 2 - 27 3}{15})

= 2 (3 + \frac{2 2 - 27 3}{15})

グラフ

人気の例

derivative (x^2-49)/(x+7)

d er i v a t i v e \frac{x ^{2} - 49}{x + 7}

integral of (3x)/(sqrt(9-25x^4))

\int \frac{3 x}{9 - 25 x ^{4}} d x

derivative f(x)=(x^2+3)^3(x^3+3)^2

d er i v a t i v e f (x) = (x^{2} + 3)^{3} (x^{3} + 3)^{2}

derivative of 5x^2cos(7x)

\frac{d}{d x} (5 x^{2} cos (7 x))

f^{''}(x)=x^3-4x+1,f^'(0)=2,f(1)=-2

f^{^{''}} (x) = x^{3} - 4 x + 1, f^{^{'}} (0) = 2, f (1) = - 2