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受欢迎的微积分 >

integral from 1 to 4 of 7e^{sqrt(x)}

解答

\int_{1}^{4} 7 e^{x} d x

解答

14 e^{2}

+1

十进制

103.44678 \dots

求解步骤

\int_{1}^{4} 7 e^{x} d x

提出常数:

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

= 7 \cdot \int_{1}^{4} e^{x} d x

使用换元积分法

= 7 \cdot \int_{1}^{2} e^{u} \cdot 2 u d u

提出常数:

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

= 7 \cdot 2 \cdot \int_{1}^{2} e^{u} u d u

使用分布积分法

= 7 \cdot 2 [e^{u} u - \int e^{u} d u]_{1}^{2}

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

= 7 \cdot 2 [e^{u} u - e^{u}]_{1}^{2}

化简

= 14 [e^{u} u - e^{u}]_{1}^{2}

带入上下限计算后得:

e^{2}

= 14 e^{2}

作图

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