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…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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…