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受欢迎的微积分 >

integral from 0 to 6 of 6sin(0.3t)

解答

\int_{0}^{6} 6 sin (0.3 t) d t

解答

24.54404 \dots

求解步骤

\int_{0}^{6} 6 sin (0.3 t) d t

提出常数:

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

= 6 \cdot \int_{0}^{6} sin (0.3 t) d t

使用换元积分法

= 6 \cdot \int_{0}^{1.8} sin (u) \frac{1}{0.3} d u

提出常数:

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

= 6 \cdot \frac{1}{0.3} \cdot \int_{0}^{1.8} sin (u) d u

化简

= 6 \cdot 3.33333 \dots \cdot \int_{0}^{1.8} sin (u) d u

使用积分常见定则:

\int sin (u) d u = - cos (u)

= 6 \cdot 3.33333 \dots [- cos (u)]_{0}^{1.8}

化简

= 20 [- cos (u)]_{0}^{1.8}

带入上下限计算后得:

1.22720 \dots

= 20 \cdot 1.22720 \dots

化简

= 24.54404 \dots

作图

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