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Popular Calculus >

area y=x,y=2x,y=-x+4

Solution

area

y = x, y = 2 x, y = - x + 4

Solution

\frac{4}{3}

+1

Decimal

1.33333 \dots

Solution steps

To find the intersection points solve

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

x = 2 x : x = 0

x = - x + 4 : x = 2

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

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

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

\int_{0}^{\frac{4}{3}} ∣ x - 2 x ∣ d x = \frac{8}{9}

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

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

Simplify

= \frac{4}{3}

Graph

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Frequently Asked Questions (FAQ)

What is area y=x,y=2x,y=-x+4 ?
The answer to area y=x,y=2x,y=-x+4 is 4/3