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受欢迎的微积分 >

integral of 3cos(x/2)

解答

\int 3 cos (\frac{x}{2}) d x

解答

6 sin (\frac{x}{2}) + C

求解步骤

\int 3 cos (\frac{x}{2}) d x

提出常数:

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

= 3 \cdot \int cos (\frac{x}{2}) d x

使用换元积分法

= 3 \cdot \int cos (u) \cdot 2 d u

提出常数:

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

= 3 \cdot 2 \cdot \int cos (u) d u

使用积分常见定则:

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

= 3 \cdot 2 sin (u)

u = \frac{x}{2}

代回

= 3 \cdot 2 sin (\frac{x}{2})

化简

= 6 sin (\frac{x}{2})

解答补常数

= 6 sin (\frac{x}{2}) + C

作图

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