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受欢迎的微积分 >

integral of ((2-x)^3)/3

解答

\int \frac{( 2 - x ) ^{3}}{3} d x

解答

- \frac{1}{12} (2 - x)^{4} + C

求解步骤

\int \frac{( 2 - x ) ^{3}}{3} d x

提出常数:

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

= \frac{1}{3} \cdot \int (2 - x)^{3} d x

使用换元积分法

= \frac{1}{3} \cdot \int - u^{3} d u

提出常数:

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

= \frac{1}{3} (- \int u^{3} d u)

使用幂法则

= \frac{1}{3} (- \frac{u ^{4}}{4})

u = 2 - x

代回

= \frac{1}{3} (- \frac{( 2 - x ) ^{4}}{4})

化简

\frac{1}{3} (- \frac{( 2 - x ) ^{4}}{4}) : - \frac{1}{12} (2 - x)^{4}

= - \frac{1}{12} (2 - x)^{4}

解答补常数

= - \frac{1}{12} (2 - x)^{4} + C

作图

流行的例子

(dy)/(dx)= 4/(x^2-1)

\frac{d y}{d x} = \frac{4}{x ^{2} - 1}

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x \to 1 + lim (\frac{1 + x}{1 - x})

derivative of 6e

\frac{d}{d x} (6 e)

integral of (-4x-10)/(x^3)

\int \frac{- 4 x - 10}{x ^{3}} d x

面积 f(x)=x^2-12,g(x)=x-6,x=-2,x=3

a re a f (x) = x^{2} - 12, g (x) = x - 6, x = - 2, x = 3