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Popular >

area x=y^2-15,x=2y

Solution

area

x = y^{2} - 15, x = 2 y

Solution

\frac{256}{3}

+1

Decimal

85.33333 \dots

Solution steps

Isolate

y

for

x = y^{2} - 15 : y = x + 15, y = - x + 15

Isolate

y

for

x = 2 y : y = \frac{x}{2}

f_{1} (x) = x + 15

f_{2} (x) = - x + 15

To find the intersection points solve

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

x + 15 = - x + 15 : x = - 15

x + 15 = \frac{x}{2} : x = 10

- x + 15 = \frac{x}{2} : x = - 6

= \int_{- 15}^{- 6} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{- 6}^{10} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 15}^{- 6} x + 15 - (- x + 15) d x + \int_{- 6}^{10} x + 15 - \frac{x}{2} d x

\int_{- 15}^{- 6} x + 15 - (- x + 15) d x = 36

\int_{- 6}^{10} x + 15 - \frac{x}{2} d x = \frac{148}{3}

= 36 + \frac{148}{3}

Simplify

= \frac{256}{3}

Graph

Popular Examples

limit as t approaches 0 of 18(1.15)^t

t \to 0 lim (18 (1.15)^{t})

tangent of f(x)=x^4+3e^x,(0,3)tangent of

f (x) = x^{4} + 3 e^{x}, (0, 3)

(\partial)/(\partial y)((xy)^{1/2})

\frac{\partial}{\partial y} ((x y)^{\frac{1}{2}})

derivative of 1/(8y^2)derivative of

\frac{1}{8 y ^{2}}

derivative of (arctan(6x)^2)

\frac{d}{d x} ((arctan (6 x))^{2})

Frequently Asked Questions (FAQ)

What is area x=y^2-15,x=2y ?
The answer to area x=y^2-15,x=2y is 256/3