integral from-3 to 3 of (e^{x+3})

解答

\int_{- 3}^{3} (e^{x + 3}) d x

e^{6} - 1

十进制

402.42879 \dots

求解步骤

\int_{- 3}^{3} e^{x + 3} d x

e^{x + 3} = e^{3} e^{x}

= \int_{- 3}^{3} e^{3} e^{x} d x

提出常数:

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

= e^{3} \cdot \int_{- 3}^{3} e^{x} d x

使用积分常见定则:

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

= e^{3} [e^{x}]_{- 3}^{3}

带入上下限计算后得:

e^{3} - \frac{1}{e ^{3}}

= e^{3} (e^{3} - \frac{1}{e ^{3}})

化简

= e^{6} - 1

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