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受欢迎的微积分 >

integral from 0 to 1 of 6cos(3x)

解答

\int_{0}^{1} 6 cos (3 x) d x

解答

2 sin (3)

+1

十进制

0.28224 \dots

求解步骤

\int_{0}^{1} 6 cos (3 x) d x

提出常数:

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

= 6 \cdot \int_{0}^{1} cos (3 x) d x

使用换元积分法

= 6 \cdot \int_{0}^{3} cos (u) \frac{1}{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}{3} \cdot \int_{0}^{3} cos (u) d u

使用积分常见定则:

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

= 6 \cdot \frac{1}{3} [sin (u)]_{0}^{3}

化简

6 \cdot \frac{1}{3} [sin (u)]_{0}^{3} : 2 [sin (u)]_{0}^{3}

= 2 [sin (u)]_{0}^{3}

带入上下限计算后得:

sin (3)

= 2 sin (3)

作图

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