What is area y=8-x,x=((y-2)^2)/3 ?

The answer to area y=8-x,x=((y-2)^2)/3 is 81/2

area y=8-x,x=((y-2)^2)/3

area

y = 8 - x, x = \frac{( y - 2 ) ^{2}}{3}

\frac{81}{2}

Decimal

40.5

Solution steps

Isolate

y

for

x = \frac{( y - 2 ) ^{2}}{3} : y = 3 x + 2, y = - 3 x + 2

f_{1} (x) = 8 - x

f_{2} (x) = 3 x + 2

To find the intersection points solve

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

8 - x = 3 x + 2 : x = 3

8 - x = - 3 x + 2 : x = 12

3 x + 2 = - 3 x + 2 : x = 0

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

= \int_{0}^{3} 3 x + 2 - (- 3 x + 2) d x + \int_{3}^{12} 8 - x - (- 3 x + 2) d x

\int_{0}^{3} 3 x + 2 - (- 3 x + 2) d x = 12

\int_{3}^{12} 8 - x - (- 3 x + 2) d x = \frac{57}{2}

= 12 + \frac{57}{2}

Simplify

= \frac{81}{2}

\int e^{x} e^{- x} d x

y^{^{''}} + y^{^{'}} - 6 y = 0, y (0) = 1

\frac{\partial}{\partial x} (4 x (x^{2} + y^{2}) - 4 x)

t \to 1 lim (sin (3 π t))

t an g e n t y = x^{2} - 7, (- 5, 18)

What is area y=8-x,x=((y-2)^2)/3 ?
The answer to area y=8-x,x=((y-2)^2)/3 is 81/2