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Popular >

area x+2y=7,x+8=y^2

Solution

area

x + 2 y = 7, x + 8 = y^{2}

Solution

\frac{256}{3}

+1

Decimal

85.33333 \dots

Solution steps

Isolate

y

for

x + 2 y = 7 : y = \frac{7 - x}{2}

Isolate

y

for

x + 8 = y^{2} : y = x + 8, y = - x + 8

f_{1} (x) = \frac{7 - x}{2}

f_{2} (x) = x + 8

To find the intersection points solve

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

\frac{7 - x}{2} = x + 8 : x = 1

\frac{7 - x}{2} = - x + 8 : x = 17

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

= \int_{- 8}^{1} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{1}^{17} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 8}^{1} x + 8 - (- x + 8) d x + \int_{1}^{17} \frac{7 - x}{2} - (- x + 8) d x

\int_{- 8}^{1} x + 8 - (- x + 8) d x = 36

\int_{1}^{17} \frac{7 - x}{2} - (- x + 8) d x = \frac{148}{3}

= 36 + \frac{148}{3}

Simplify

= \frac{256}{3}

Graph

Popular Examples

integral of 14x^6y^{-4}-12x^5y^{-3}

\int 14 x^{6} y^{- 4} - 12 x^{5} y^{- 3} d x

limit as x approaches 3 of sqrt(12-x)-3

x \to 3 lim (12 - x - 3)

limit as x approaches infinity of (1+(2/x))^{(x/4)}

x \to \infty lim ((1 + (\frac{2}{x}))^{(\frac{x}{4})})

integral from 0 to 3 of x^3-5x

\int_{0}^{3} x^{3} - 5 x d x

(dy)/(dx)= 1/7 sqrt(y)cos^2(sqrt(y))

\frac{d y}{d x} = \frac{1}{7} y cos^{2} (y)

Frequently Asked Questions (FAQ)

What is area x+2y=7,x+8=y^2 ?
The answer to area x+2y=7,x+8=y^2 is 256/3