What is area x,x=8-1/4 y^2 ?

The answer to area x,x=8-1/4 y^2 is 72

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area x,x=8-1/4 y^2

area

x, x = 8 - \frac{1}{4} y^{2}

72

Solution steps

Isolate

y

for

x = 8 - \frac{1}{4} y^{2} : y = 2 - x + 8, y = - 2 - x + 8

f_{1} (x) = 2 - x + 8

f_{2} (x) = - 2 - x + 8

To find the intersection points solve

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

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

2 - x + 8 = x : x = 4

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

= \int_{- 8}^{4} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{4}^{8} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{- 8}^{4} - 2 - x + 8 - x d x + \int_{4}^{8} 2 - x + 8 - (- 2 - x + 8) d x

\int_{- 8}^{4} - 2 - x + 8 - x d x = \frac{152}{3}

\int_{4}^{8} 2 - x + 8 - (- 2 - x + 8) d x = \frac{64}{3}

= \frac{152}{3} + \frac{64}{3}

Simplify

= 72

\frac{\partial}{\partial x} (x^{y})

\int - e^{2 x} x d x

\frac{\partial}{\partial x} (y^{6} cos (3 x))

\int \frac{x ^{3}}{3 ( 1 + x ^{2} )} d x

f (x) = 3 x^{2} - 4 x, at x = - 1