What is area y=1.25x,x=8.5-y^2 ?

The answer to area y=1.25x,x=8.5-y^2 is 33.97938…

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area y=1.25x,x=8.5-y^2

area

y = 1.25 x, x = 8.5 - y^{2}

33.97938 \dots

Solution steps

Isolate

y

for

x = 8.5 - y^{2} : y = - x + 8.5, y = - - x + 8.5

f_{1} (x) = 1.25 x

f_{2} (x) = - x + 8.5

To find the intersection points solve

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

1.25 x = - x + 8.5 : x = \frac{- 1 + 54.125}{3.125}

1.25 x = - - x + 8.5 : x = \frac{- 1 - 54.125}{3.125}

- x + 8.5 = - - x + 8.5 : x = 8.5

= \int_{\frac{- 1 - 54.125}{3.125}}^{\frac{- 1 + 54.125}{3.125}} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{\frac{- 1 + 54.125}{3.125}}^{8.5} ∣ f_{3} (x) - f_{2} (x) ∣ d x

= \int_{\frac{- 1 - 54.125}{3.125}}^{\frac{- 1 + 54.125}{3.125}} 1.25 x - (- - x + 8.5) d x + \int_{\frac{- 1 + 54.125}{3.125}}^{8.5} - - x + 8.5 - - x + 8.5 d x

\int_{\frac{- 1 - 54.125}{3.125}}^{\frac{- 1 + 54.125}{3.125}} 1.25 x - (- - x + 8.5) d x = 12.05794 \dots

\int_{\frac{- 1 + 54.125}{3.125}}^{8.5} - - x + 8.5 - - x + 8.5 d x = 21.92144 \dots

= 12.05794 \dots + 21.92144 \dots

Simplify

= 33.97938 \dots

\frac{d}{d x} (48 x (4 x^{2} + 9)^{5})

f (x) = \frac{4 x - 3}{3 x + 2} + x^{3}

\int \frac{x ^{2} + 4 x - 5}{x ^{3} - 1} d x

f (x) = 1680 (2 x + 5)^{4}

x arcsin (x) + 1 - x^{2}

What is area y=1.25x,x=8.5-y^2 ?
The answer to area y=1.25x,x=8.5-y^2 is 33.97938…