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Popular >

area x=3y,x=y^2-4

Solution

area

x = 3 y, x = y^{2} - 4

Solution

\frac{125}{6}

+1

Decimal Notation

20.83333 \dots

Solution steps

Isolate

y

for

x = 3 y : y = \frac{x}{3}

Isolate

y

for

x = y^{2} - 4 : y = x + 4, y = - x + 4

f_{1} (x) = \frac{x}{3}

f_{2} (x) = x + 4

To find the intersection points solve

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

\frac{x}{3} = x + 4 : x = 12

\frac{x}{3} = - x + 4 : x = - 3

x + 4 = - x + 4 : x = - 4

= \int_{- 4}^{- 3} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{- 3}^{12} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{- 4}^{- 3} x + 4 - (- x + 4) d x + \int_{- 3}^{12} \frac{x}{3} - x + 4 d x

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

\int_{- 3}^{12} \frac{x}{3} - x + 4 d x = \frac{39}{2}

= \frac{4}{3} + \frac{39}{2}

Simplify

= \frac{125}{6}

Popular Examples

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\int x^{2} e^{- λ x} d x

integral from 0 to 1 of 3/(1+t^2)

\int_{0}^{1} \frac{3}{1 + t ^{2}} d t

d/(dθ)(3-sin(θ))

\frac{d}{d θ} (3 - sin (θ))

tangent of f(x)=x^2-4,\at x=0 tangent of

f (x) = x^{2} - 4, at x = 0

derivative of (3x^4+1/(x^3))

\frac{d}{d x} (\frac{3 x ^{4} + 1}{x ^{3}})

Frequently Asked Questions (FAQ)

What is area x=3y,x=y^2-4 ?
The answer to area x=3y,x=y^2-4 is 125/6