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受欢迎的微积分 >

integral of 4sin(2θ)

解答

\int 4 sin (2 θ) d θ

解答

- 2 cos (2 θ) + C

求解步骤

\int 4 sin (2 θ) d θ

提出常数:

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

= 4 \cdot \int sin (2 θ) d θ

使用换元积分法

= 4 \cdot \int sin (u) \frac{1}{2} d u

提出常数:

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

= 4 \cdot \frac{1}{2} \cdot \int sin (u) d u

使用积分常见定则:

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

= 4 \cdot \frac{1}{2} (- cos (u))

u = 2 θ

代回

= 4 \cdot \frac{1}{2} (- cos (2 θ))

化简

4 \cdot \frac{1}{2} (- cos (2 θ)) : - 2 cos (2 θ)

= - 2 cos (2 θ)

解答补常数

= - 2 cos (2 θ) + C

作图

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