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受欢迎的微积分 >

integral from 0 to 1 of (u+3)(u-4)

解答

\int_{0}^{1} (u + 3) (u - 4) d u

解答

- \frac{73}{6}

+1

十进制

- 12.16666 \dots

求解步骤

\int_{0}^{1} (u + 3) (u - 4) d u

乘开

(u + 3) (u - 4) : u^{2} - u - 12

= \int_{0}^{1} u^{2} - u - 12 d u

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} u^{2} d u - \int_{0}^{1} u d u - \int_{0}^{1} 12 d u

\int_{0}^{1} u^{2} d u = \frac{1}{3}

\int_{0}^{1} u d u = \frac{1}{2}

\int_{0}^{1} 12 d u = 12

= \frac{1}{3} - \frac{1}{2} - 12

化简

\frac{1}{3} - \frac{1}{2} - 12 : - \frac{73}{6}

= - \frac{73}{6}

作图

流行的例子

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d er i v a t i v e f (x) = 3 x^{\frac{5}{4}}

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y^{2} d x + x y d y = 0

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d er i v a t i v e x (3 x + 4)^{5}

y=(x^2-2x+2)e^x

y = (x^{2} - 2 x + 2) e^{x}