What is area y=5x,y= 5/2 x,y=84-x^2 ?

The answer to area y=5x,y= 5/2 x,y=84-x^2 is 10955/48

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area y=5x,y= 5/2 x,y=84-x^2

area

y = 5 x, y = \frac{5}{2} x, y = 84 - x^{2}

\frac{10955}{48}

Decimal

228.22916 \dots

Solution steps

To find the intersection points solve

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

5 x = \frac{5}{2} x : x = 0

5 x = 84 - x^{2} : x = - 12, x = 7

\frac{5}{2} x = 84 - x^{2} : x = - \frac{21}{2}, x = 8

= \int_{- 12}^{- \frac{21}{2}} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{- \frac{21}{2}}^{0} ∣ f_{2} (x) - f_{1} (x) ∣ d x + \int_{0}^{7} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{7}^{8} ∣ f_{2} (x) - f_{3} (x) ∣ d x

= \int_{- 12}^{- \frac{21}{2}} 5 x - (84 - x^{2}) d x + \int_{- \frac{21}{2}}^{0} \frac{5}{2} x - 5 x d x + \int_{0}^{7} 5 x - \frac{5}{2} x d x + \int_{7}^{8} \frac{5}{2} x - (84 - x^{2}) d x

\int_{- 12}^{- \frac{21}{2}} 5 x - (84 - x^{2}) d x = \frac{81}{4}

\int_{- \frac{21}{2}}^{0} \frac{5}{2} x - 5 x d x = \frac{2205}{16}

\int_{0}^{7} 5 x - \frac{5}{2} x d x = \frac{245}{4}

\int_{7}^{8} \frac{5}{2} x - (84 - x^{2}) d x = \frac{107}{12}

= \frac{81}{4} + \frac{2205}{16} + \frac{245}{4} + \frac{107}{12}

Simplify

= \frac{10955}{48}

What is area y=5x,y= 5/2 x,y=84-x^2 ?
The answer to area y=5x,y= 5/2 x,y=84-x^2 is 10955/48