What is area y=9x,y= 3/7 x,y=52-x^2 ?

The answer to area y=9x,y= 3/7 x,y=52-x^2 is 194550/343

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area y=9x,y= 3/7 x,y=52-x^2

area

y = 9 x, y = \frac{3}{7} x, y = 52 - x^{2}

\frac{194550}{343}

Decimal Notation

567.20116 \dots

Solution steps

To find the intersection points solve

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

9 x = \frac{3}{7} x : x = 0

9 x = 52 - x^{2} : x = - 13, x = 4

\frac{3}{7} x = 52 - x^{2} : x = - \frac{52}{7}, x = 7

= \int_{- 13}^{- \frac{52}{7}} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{- \frac{52}{7}}^{0} ∣ f_{2} (x) - f_{1} (x) ∣ d x + \int_{0}^{4} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{4}^{7} ∣ f_{2} (x) - f_{3} (x) ∣ d x

= \int_{- 13}^{- \frac{52}{7}} 9 x - (52 - x^{2}) d x + \int_{- \frac{52}{7}}^{0} \frac{3}{7} x - 9 x d x + \int_{0}^{4} 9 x - \frac{3}{7} x d x + \int_{4}^{7} \frac{3}{7} x - (52 - x^{2}) d x

\int_{- 13}^{- \frac{52}{7}} 9 x - (52 - x^{2}) d x = \frac{141453}{686}

\int_{- \frac{52}{7}}^{0} \frac{3}{7} x - 9 x d x = \frac{81120}{343}

\int_{0}^{4} 9 x - \frac{3}{7} x d x = \frac{480}{7}

\int_{4}^{7} \frac{3}{7} x - (52 - x^{2}) d x = \frac{783}{14}

= \frac{141453}{686} + \frac{81120}{343} + \frac{480}{7} + \frac{783}{14}

Simplify

= \frac{194550}{343}

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What is area y=9x,y= 3/7 x,y=52-x^2 ?
The answer to area y=9x,y= 3/7 x,y=52-x^2 is 194550/343