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Popular Calculus >

area x+y=0,x+y^2=56

Solution

area

x + y = 0, x + y^{2} = 56

Solution

\frac{1125}{2}

+1

Decimal

562.5

Solution steps

Isolate

y

for

x + y = 0 : y = - x

Isolate

y

for

x + y^{2} = 56 : y = 56 - x, y = - 56 - x

f_{1} (x) = - x

f_{2} (x) = 56 - x

To find the intersection points solve

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

- x = 56 - x : x = - 8

- x = - 56 - x : x = 7

56 - x = - 56 - x : x = 56

= \int_{- 8}^{7} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{7}^{56} ∣ f_{2} (x) - f_{3} (x) ∣ d x

= \int_{- 8}^{7} - x - 56 - x d x + \int_{7}^{56} 56 - x - (- 56 - x) d x

\int_{- 8}^{7} - x - 56 - x d x = \frac{631}{6}

\int_{7}^{56} 56 - x - (- 56 - x) d x = \frac{1372}{3}

= \frac{631}{6} + \frac{1372}{3}

Simplify

= \frac{1125}{2}

Graph

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Frequently Asked Questions (FAQ)

What is area x+y=0,x+y^2=56 ?
The answer to area x+y=0,x+y^2=56 is 1125/2