integral from-5 to 4 of e^{x+4}

解答

\int_{- 5}^{4} e^{x + 4} d x

e^{8} - \frac{1}{e}

十进制

2980.59010 \dots

求解步骤

\int_{- 5}^{4} e^{x + 4} d x

e^{x + 4} = e^{4} e^{x}

= \int_{- 5}^{4} e^{4} e^{x} d x

提出常数:

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

= e^{4} \cdot \int_{- 5}^{4} e^{x} d x

使用积分常见定则:

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

= e^{4} [e^{x}]_{- 5}^{4}

带入上下限计算后得:

e^{4} - \frac{1}{e ^{5}}

= e^{4} (e^{4} - \frac{1}{e ^{5}})

化简

= e^{8} - \frac{1}{e}

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