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受欢迎的微积分 >

integral from 0 to 1 of 34.6e^{-0.06t}

解答

\int_{0}^{1} 34.6 e^{- 0.06 t} d t

解答

33.58245 \dots

求解步骤

\int_{0}^{1} 34.6 e^{- 0.06 t} d t

提出常数:

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

= 34.6 \cdot \int_{0}^{1} e^{- 0.06 t} d t

使用换元积分法

= 34.6 \cdot \int_{0}^{- 0.06} - \frac{1}{0.06} e^{u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= 34.6 (- \int_{- 0.06}^{0} - \frac{1}{0.06} e^{u} d u)

提出常数:

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

= 34.6 (- (- \frac{1}{0.06} \cdot \int_{- 0.06}^{0} e^{u} d u))

化简

= 34.6 (- (- 16.66666 \dots \cdot \int_{- 0.06}^{0} e^{u} d u))

使用积分常见定则:

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

= 34.6 (- (- 16.66666 \dots [e^{u}]_{- 0.06}^{0}))

化简

= 576.66666 \dots [e^{u}]_{- 0.06}^{0}

带入上下限计算后得:

0.05823 \dots

= 576.66666 \dots \cdot 0.05823 \dots

化简

= 33.58245 \dots

作图

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