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受欢迎的微积分 >

integral from 3 to 6 of 10000e^{0.02t}

解答

\int_{3}^{6} 10000 e^{0.02 t} d t

解答

32830.15251 \dots

求解步骤

\int_{3}^{6} 10000 e^{0.02 t} d t

提出常数:

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

= 10000 \cdot \int_{3}^{6} e^{0.02 t} d t

使用换元积分法

= 10000 \cdot \int_{0.06}^{0.12} e^{u} \frac{1}{0.02} d u

提出常数:

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

= 10000 \cdot \frac{1}{0.02} \cdot \int_{0.06}^{0.12} e^{u} d u

化简

= 10000 \cdot 50 \cdot \int_{0.06}^{0.12} e^{u} d u

使用积分常见定则:

\int e^{u} d u = e^{u}

= 10000 \cdot 50 [e^{u}]_{0.06}^{0.12}

化简

= 500000 [e^{u}]_{0.06}^{0.12}

带入上下限计算后得:

0.06566 \dots

= 500000 \cdot 0.06566 \dots

化简

= 32830.15251 \dots

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