zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的微积分 >

integral of-1/27 sin(3x)

解答

\int - \frac{1}{27} sin (3 x) d x

解答

\frac{1}{81} cos (3 x) + C

求解步骤

\int - \frac{1}{27} sin (3 x) d x

提出常数:

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

= - \frac{1}{27} \cdot \int sin (3 x) d x

使用换元积分法

= - \frac{1}{27} \cdot \int sin (u) \frac{1}{3} d u

提出常数:

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

= - \frac{1}{27} \cdot \frac{1}{3} \cdot \int sin (u) d u

使用积分常见定则:

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

= - \frac{1}{27} \cdot \frac{1}{3} (- cos (u))

u = 3 x

代回

= - \frac{1}{27} \cdot \frac{1}{3} (- cos (3 x))

化简

- \frac{1}{27} \cdot \frac{1}{3} (- cos (3 x)) : \frac{1}{81} cos (3 x)

= \frac{1}{81} cos (3 x)

解答补常数

= \frac{1}{81} cos (3 x) + C

作图

流行的例子

integral of (3-5x)/(sqrt(9-5x^2))

\int \frac{3 - 5 x}{9 - 5 x ^{2}} d x

derivative of arccos(6/x)

\frac{d}{d x} (arccos (\frac{6}{x}))

(\partial)/(\partial v)(e^{{u}(v)}+sin(v))

\frac{\partial}{\partial v} (e^{u (v)} + sin (v))

integral from 1 to 2 of (-y^3+2y^2+5y-6)

\int_{1}^{2} (- y^{3} + 2 y^{2} + 5 y - 6) d y

integral from-3 to 3 of |2x-1|

\int_{- 3}^{3} ∣ 2 x - 1 ∣ d x