What is area y=x,y=1-x,y=-x/2 ?

The answer to area y=x,y=1-x,y=-x/2 is 3/4

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area y=x,y=1-x,y=-x/2

area

y = x, y = 1 - x, y = - \frac{x}{2}

\frac{3}{4}

Decimal Notation

0.75

Solution steps

To find the intersection points solve

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

x = 1 - x : x = \frac{1}{2}

x = - \frac{x}{2} : x = 0

1 - x = - \frac{x}{2} : x = 2

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

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

\int_{0}^{\frac{1}{2}} x - (- \frac{x}{2}) d x = \frac{3}{16}

\int_{\frac{1}{2}}^{2} - \frac{x}{2} - (1 - x) d x = \frac{9}{16}

= \frac{3}{16} + \frac{9}{16}

Simplify

= \frac{3}{4}

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