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Popular >

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

Solution

area

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

Solution

\frac{9}{2}

+1

Decimal Notation

4.5

Solution steps

Isolate

y

for

x = - y : y = - x

Isolate

y

for

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

f_{1} (x) = - x

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

To find the intersection points solve

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

- x = - x + 2 : x = - 2

- x = - - x + 2 : x = 1

- x + 2 = - - x + 2 : x = 2

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

= \int_{- 2}^{1} - x - - x + 2 d x + \int_{1}^{2} - x + 2 - (- - x + 2) d x

\int_{- 2}^{1} - x - - x + 2 d x = \frac{19}{6}

\int_{1}^{2} - x + 2 - (- - x + 2) d x = \frac{4}{3}

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

Simplify

= \frac{9}{2}

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\int \frac{1}{5 x - 2} d x

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\int \frac{1}{u ^{4}} d u

Frequently Asked Questions (FAQ)

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