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受欢迎的微积分 >

integral from 0 to 3 of 450.268e^{1.12567t}

解答

\int_{0}^{3} 450.268 e^{1.12567 t} d t

解答

11313.23346 \dots

求解步骤

\int_{0}^{3} 450.268 e^{1.12567 t} d t

提出常数:

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

= 450.268 \cdot \int_{0}^{3} e^{1.12567 t} d t

使用换元积分法

= 450.268 \cdot \int_{0}^{3.37701} e^{u} \frac{1}{1.12567} d u

提出常数:

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

= 450.268 \cdot \frac{1}{1.12567} \cdot \int_{0}^{3.37701} e^{u} d u

化简

= 450.268 \cdot 0.88835 \dots \cdot \int_{0}^{3.37701} e^{u} d u

使用积分常见定则:

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

= 450.268 \cdot 0.88835 \dots [e^{u}]_{0}^{3.37701}

化简

= 400 [e^{u}]_{0}^{3.37701}

带入上下限计算后得:

28.28308 \dots

= 400 \cdot 28.28308 \dots

化简

= 11313.23346 \dots

作图

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