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 from 0 to 6 of 6sin(0.3x)

解答

\int_{0}^{6} 6 sin (0.3 x) d x

解答

24.54404 \dots

求解步骤

\int_{0}^{6} 6 sin (0.3 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}^{6} sin (0.3 x) d x

使用换元积分法

= 6 \cdot \int_{0}^{1.8} sin (u) \frac{1}{0.3} d u

提出常数:

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

= 6 \cdot \frac{1}{0.3} \cdot \int_{0}^{1.8} sin (u) d u

化简

= 6 \cdot 3.33333 \dots \cdot \int_{0}^{1.8} sin (u) d u

使用积分常见定则:

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

= 6 \cdot 3.33333 \dots [- cos (u)]_{0}^{1.8}

化简

= 20 [- cos (u)]_{0}^{1.8}

带入上下限计算后得:

1.22720 \dots

= 20 \cdot 1.22720 \dots

化简

= 24.54404 \dots

作图

流行的例子

integral from-sqrt(3) to-1 of arctan(x)

\int_{- 3}^{- 1} arctan (x) d x

integral from-1 to 1 of 2x-1

\int_{- 1}^{1} 2 x - 1 d x

integral from 0 to infinity of x/(x+1)

\int_{0}^{\infty} \frac{x}{x + 1} d x

integral from 0 to x of (t^3+3t^2+2)

\int_{0}^{x} (t^{3} + 3 t^{2} + 2) d t

integral from 3 to 10 of (5x^2-8)/3

\int_{3}^{10} \frac{5 x ^{2} - 8}{3} d x