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受欢迎的微积分 >

integral of 7sin(θ/3)

解答

\int 7 sin (\frac{θ}{3}) d θ

解答

- 21 cos (\frac{θ}{3}) + C

求解步骤

\int 7 sin (\frac{θ}{3}) d θ

提出常数:

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

= 7 \cdot \int sin (\frac{θ}{3}) d θ

使用换元积分法

= 7 \cdot \int sin (u) \cdot 3 d u

提出常数:

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

= 7 \cdot 3 \cdot \int sin (u) d u

使用积分常见定则:

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

= 7 \cdot 3 (- cos (u))

u = \frac{θ}{3}

代回

= 7 \cdot 3 (- cos (\frac{θ}{3}))

化简

= - 21 cos (\frac{θ}{3})

解答补常数

= - 21 cos (\frac{θ}{3}) + C

作图

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