What is area x=1-y^2,-x-1 ?

The answer to area x=1-y^2,-x-1 is 9/2

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area x=1-y^2,-x-1

area

x = 1 - y^{2}, - x - 1

\frac{9}{2}

Decimal Notation

4.5

Solution steps

Isolate

y

for

x = 1 - y^{2} : y = - x + 1, y = - - x + 1

f_{1} (x) = - x + 1

f_{2} (x) = - - x + 1

To find the intersection points solve

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

- x + 1 = - - x + 1 : x = 1

- x + 1 = - x - 1 : x = - 3

- - x + 1 = - x - 1 : x = 0

= \int_{- 3}^{0} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{0}^{1} ∣ f_{2} (x) - f_{1} (x) ∣ d x

= \int_{- 3}^{0} - x + 1 - (- x - 1) d x + \int_{0}^{1} - - x + 1 - - x + 1 d x

\int_{- 3}^{0} - x + 1 - (- x - 1) d x = \frac{19}{6}

\int_{0}^{1} - - x + 1 - - x + 1 d x = \frac{4}{3}

= \frac{19}{6} + \frac{4}{3}

Simplify

= \frac{9}{2}

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