What is area y^2-2x=2,x-y=3 ?

The answer to area y^2-2x=2,x-y=3 is 18

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area y^2-2x=2,x-y=3

area

y^{2} - 2 x = 2, x - y = 3

18

Solution steps

Isolate

y

for

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

Isolate

y

for

x - y = 3 : y = - 3 + x

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

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

To find the intersection points solve

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

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

2 + 2 x = - 3 + x : x = 7

- 2 + 2 x = - 3 + x : x = 1

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

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

\int_{- 1}^{1} 2 + 2 x - (- 2 + 2 x) d x = \frac{16}{3}

\int_{1}^{7} 2 + 2 x - (- 3 + x) d x = \frac{38}{3}

= \frac{16}{3} + \frac{38}{3}

Simplify

= 18

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

\int \frac{4 x + 6}{x ^{2} + 3 x + 1} d x

y = \frac{( 2 x ^{2} + 7 )}{x ^{2} + 3}

x \to 3 π + lim (csc (x))

f (x) = - \frac{5}{x ^{2}}