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Popular >

area x=10-2y,x=y^2+2

Solution

area

x = 10 - 2 y, x = y^{2} + 2

Solution

36

Solution steps

Isolate

y

for

x = 10 - 2 y : y = - \frac{x - 10}{2}

Isolate

y

for

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

f_{1} (x) = - \frac{x - 10}{2}

f_{2} (x) = x - 2

To find the intersection points solve

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

- \frac{x - 10}{2} = x - 2 : x = 6

- \frac{x - 10}{2} = - x - 2 : x = 18

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

= \int_{2}^{6} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{6}^{18} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{2}^{6} x - 2 - (- x - 2) d x + \int_{6}^{18} - \frac{x - 10}{2} - (- x - 2) d x

\int_{2}^{6} x - 2 - (- x - 2) d x = \frac{32}{3}

\int_{6}^{18} - \frac{x - 10}{2} - (- x - 2) d x = \frac{76}{3}

= \frac{32}{3} + \frac{76}{3}

Simplify

= 36

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Frequently Asked Questions (FAQ)

What is area x=10-2y,x=y^2+2 ?
The answer to area x=10-2y,x=y^2+2 is 36