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 4x=4y-y^2,4x-y=0

解答

面积

4 x = 4 y - y^{2}, 4 x - y = 0

解答

\frac{9}{8}

+1

十进制

1.125

求解步骤

对于

4 x = 4 y - y^{2}

将

y

移到一边:

y = - 2 (- x + 1 - 1), y = 2 (- x + 1 + 1)

对于

4 x - y = 0

将

y

移到一边:

y = 4 x

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

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

要找到相交点，解

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

- 2 (- x + 1 - 1) = 2 (- x + 1 + 1) : x = 1

- 2 (- x + 1 - 1) = 4 x : x = 0

2 (- x + 1 + 1) = 4 x : x = \frac{3}{4}

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

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

\int_{0}^{\frac{3}{4}} - 2 (- x + 1 - 1) - 4 x d x = \frac{19}{24}

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

= \frac{19}{24} + \frac{1}{3}

化简

= \frac{9}{8}

作图

流行的例子

integral of 1/(x^2sqrt(7+x^2))

\int \frac{1}{x ^{2} 7 + x ^{2}} d x

derivative f(x)=e^{7x}cos(10x)

d er i v a t i v e f (x) = e^{7 x} cos (10 x)

integral from-1 to 1 of x^2(1.5x^2)

\int_{- 1}^{1} x^{2} (1.5 x^{2}) d x

derivative sqrt(a*t)(8-a)+8a

d er i v a t i v e a \cdot t (8 - a) + 8 a

integral of (xln(x^2+1)+(x^2+1)y)

\int (x ln (x^{2} + 1) + (x^{2} + 1) y) d x