What is area x,4x,-x+22 ?

The answer to area x,4x,-x+22 is 363/5

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area x,4x,-x+22

area

x, 4 x, - x + 22

\frac{363}{5}

Decimal

72.6

Solution steps

To find the intersection points solve

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

x = 4 x : x = 0

x = - x + 22 : x = 11

4 x = - x + 22 : x = \frac{22}{5}

= \int_{0}^{\frac{22}{5}} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{\frac{22}{5}}^{11} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{0}^{\frac{22}{5}} ∣ x - 4 x ∣ d x + \int_{\frac{22}{5}}^{11} ∣ x - (- x + 22) ∣ d x

\int_{0}^{\frac{22}{5}} ∣ x - 4 x ∣ d x = \frac{726}{25}

\int_{\frac{22}{5}}^{11} ∣ x - (- x + 22) ∣ d x = \frac{1089}{25}

= \frac{726}{25} + \frac{1089}{25}

Simplify

= \frac{363}{5}

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