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Popular >

area x=4y,x=y^2-5

Solution

area

x = 4 y, x = y^{2} - 5

Solution

36

Solution steps

Isolate

y

for

x = 4 y : y = \frac{x}{4}

Isolate

y

for

x = y^{2} - 5 : y = x + 5, y = - x + 5

f_{1} (x) = \frac{x}{4}

f_{2} (x) = x + 5

To find the intersection points solve

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

\frac{x}{4} = x + 5 : x = 20

\frac{x}{4} = - x + 5 : x = - 4

x + 5 = - x + 5 : x = - 5

= \int_{- 5}^{- 4} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{- 4}^{20} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{- 5}^{- 4} x + 5 - (- x + 5) d x + \int_{- 4}^{20} \frac{x}{4} - x + 5 d x

\int_{- 5}^{- 4} x + 5 - (- x + 5) d x = \frac{4}{3}

\int_{- 4}^{20} \frac{x}{4} - x + 5 d x = \frac{104}{3}

= \frac{4}{3} + \frac{104}{3}

Simplify

= 36

Graph

Popular Examples

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\int_{- 4}^{4} (2 x^{7} + 1) d x

derivative of (1/(y^2)-9/(y^4))(y+3y^3)derivative of

(\frac{1}{y ^{2}} - \frac{9}{y ^{4}}) (y + 3 y^{3})

integral from 2 to 4 of f(x)

\int_{2}^{4} f (x) d x

f^{^{'}} (x) = \frac{4}{x}

d/(dt)(sin(6t))

\frac{d}{d t} (sin (6 t))

Frequently Asked Questions (FAQ)

What is area x=4y,x=y^2-5 ?
The answer to area x=4y,x=y^2-5 is 36