en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

area x,5x,-x+4

Solution

area

x, 5 x, - x + 4

Solution

\frac{8}{3}

+1

Decimal

2.66666 \dots

Solution steps

To find the intersection points solve

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

x = 5 x : x = 0

x = - x + 4 : x = 2

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

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

= \int_{0}^{\frac{2}{3}} ∣ x - 5 x ∣ d x + \int_{\frac{2}{3}}^{2} ∣ x - (- x + 4) ∣ d x

\int_{0}^{\frac{2}{3}} ∣ x - 5 x ∣ d x = \frac{8}{9}

\int_{\frac{2}{3}}^{2} ∣ x - (- x + 4) ∣ d x = \frac{16}{9}

= \frac{8}{9} + \frac{16}{9}

Simplify

= \frac{8}{3}

Graph

Popular Examples

derivative of x^4-x

derivative of 1/x+1/(x^2)+1/(x^3)

integral of 9sin^2(x)cos^2(x)

(dy)/(dx)=(2xy)/(x^2+1)

derivative of e^{2x}-1

Frequently Asked Questions (FAQ)

What is area x,5x,-x+4 ?
The answer to area x,5x,-x+4 is 8/3