What is area y=x,y=2x,y=-x+2 ?

The answer to area y=x,y=2x,y=-x+2 is 1/3

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

area

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

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

To find the intersection points solve

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

x = 2 x : x = 0

x = - x + 2 : x = 1

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

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

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

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

\int_{\frac{2}{3}}^{1} ∣ x - (- x + 2) ∣ d x = \frac{1}{9}

= \frac{2}{9} + \frac{1}{9}

Simplify

= \frac{1}{3}

\frac{d}{d x} (72 x^{2})

y^{^{''}} + 3 y^{^{'}} + 2 y = x

f (x) = 5 x^{2} - 8 x, at x = 1

x \to 2 lim (a x + b)

\frac{2 x ^{2}}{x ^{2} - 1}