What is area x+y^2=56,x=y ?

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

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

area

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

\frac{1125}{2}

Decimal

562.5

Solution steps

Isolate

y

for

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

Isolate

y

for

x = y : y = x

f_{1} (x) = 56 - x

f_{2} (x) = - 56 - x

To find the intersection points solve

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

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

56 - x = x : x = 7

- 56 - x = x : x = - 8

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

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

\int_{- 8}^{7} - 56 - x - 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}

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