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受欢迎的微积分 >

integral from 0 to 40 of 3000e^{0.04t}

解答

\int_{0}^{40} 3000 e^{0.04 t} d t

解答

296477.43182 \dots

求解步骤

\int_{0}^{40} 3000 e^{0.04 t} d t

提出常数:

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

= 3000 \cdot \int_{0}^{40} e^{0.04 t} d t

使用换元积分法

= 3000 \cdot \int_{0}^{1.6} e^{u} \frac{1}{0.04} d u

提出常数:

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

= 3000 \cdot \frac{1}{0.04} \cdot \int_{0}^{1.6} e^{u} d u

化简

= 3000 \cdot 25 \cdot \int_{0}^{1.6} e^{u} d u

使用积分常见定则:

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

= 3000 \cdot 25 [e^{u}]_{0}^{1.6}

化简

= 75000 [e^{u}]_{0}^{1.6}

带入上下限计算后得:

3.95303 \dots

= 75000 \cdot 3.95303 \dots

化简

= 296477.43182 \dots

作图

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