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受欢迎的微积分 >

integral from 2 to 7 of 700xsqrt(3+2x)

解答

\int_{2}^{7} 700 x 3 + 2 x d x

解答

1428017 - 9807

+1

十进制

56285.11204 \dots

求解步骤

\int_{2}^{7} 700 x 3 + 2 x d x

提出常数:

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

= 700 \cdot \int_{2}^{7} x 3 + 2 x d x

使用换元积分法

= 700 \cdot \int_{7}^{17} \frac{u ( u - 3 )}{4} d u

提出常数:

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

= 700 \cdot \frac{1}{4} \cdot \int_{7}^{17} u (u - 3) d u

乘开

u (u - 3) : u^{\frac{3}{2}} - 3 u

= 700 \cdot \frac{1}{4} \cdot \int_{7}^{17} u^{\frac{3}{2}} - 3 u 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

= 700 \cdot \frac{1}{4} (\int_{7}^{17} u^{\frac{3}{2}} d u - \int_{7}^{17} 3 u d u)

\int_{7}^{17} u^{\frac{3}{2}} d u = \frac{578 17 - 98 7}{5}

\int_{7}^{17} 3 u d u = 3417 - 147

= 700 \cdot \frac{1}{4} (\frac{578 17 - 98 7}{5} - (3417 - 147))

化简

700 \cdot \frac{1}{4} (\frac{578 17 - 98 7}{5} - (3417 - 147)) : 1428017 - 9807

= 1428017 - 9807

作图

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