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

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

Popular >

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

area

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

\frac{9}{2}

Decimal Notation

4.5

Solution steps

Isolate

y

for

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

Isolate

y

for

x = y : y = x

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

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

To find the intersection points solve

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

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

- x + 2 = x : x = 1

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

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

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

\int_{- 2}^{1} - - x + 2 - x 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}

y^{^{''}} - 4 y = e^{2 x}

x \to 0 lim (sin (x^{x}))

\int \frac{1}{x ^{2} + 6 x + 58} d x

f (t) = sin^{2} (e^{s i n^{2} (t)})

\frac{2}{x}, at x = \frac{1}{4}