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 >

面积 2x+y=4,y=x,y=0

解答

面积

2 x + y = 4, y = x, y = 0

解答

\frac{4}{3}

+1

十进制

1.33333 \dots

求解步骤

对于

2 x + y = 4

将

y

移到一边:

y = 4 - 2 x

f_{1} (x) = 4 - 2 x

f_{2} (x) = x

要找到相交点，解

f_{i} (x) = f_{j} (x)

4 - 2 x = x : x = \frac{4}{3}

4 - 2 x = 0 : x = 2

x = 0 : x = 0

= \int_{0}^{\frac{4}{3}} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{\frac{4}{3}}^{2} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{0}^{\frac{4}{3}} ∣ x - 0 ∣ d x + \int_{\frac{4}{3}}^{2} ∣ 4 - 2 x - 0 ∣ d x

\int_{0}^{\frac{4}{3}} ∣ x - 0 ∣ d x = \frac{8}{9}

\int_{\frac{4}{3}}^{2} ∣ 4 - 2 x - 0 ∣ d x = \frac{4}{9}

= \frac{8}{9} + \frac{4}{9}

化简

= \frac{4}{3}

作图

流行的例子

integral of 7e^{4x+e^{4x}}

\int 7 e^{4 x + e^{4 x}} d x

d/(ds)(((s-3)(s-5))/((s+1)(s+2)))

\frac{d}{d s} (\frac{( s - 3 ) ( s - 5 )}{( s + 1 ) ( s + 2 )})

\frac{d}{d t} (3 - 2 t)

derivative (1-x^2+x^4)/(x^2*sqrt(x))

d er i v a t i v e \frac{1 - x ^{2} + x ^{4}}{x ^{2} \cdot x}

limit as x approaches 0 of 0/0

x \to 0 lim (\frac{0}{0})