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Popular >

area y^2-2x=9,x-y=3

Solution

area

y^{2} - 2 x = 9, x - y = 3

Solution

\frac{128}{3}

+1

Decimal Notation

42.66666 \dots

Solution steps

Isolate

y

for

y^{2} - 2 x = 9 : y = 9 + 2 x, y = - 9 + 2 x

Isolate

y

for

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

f_{1} (x) = 9 + 2 x

f_{2} (x) = - 9 + 2 x

To find the intersection points solve

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

9 + 2 x = - 9 + 2 x : x = - \frac{9}{2}

9 + 2 x = - 3 + x : x = 8

- 9 + 2 x = - 3 + x : x = 0

= \int_{- \frac{9}{2}}^{0} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{0}^{8} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- \frac{9}{2}}^{0} 9 + 2 x - (- 9 + 2 x) d x + \int_{0}^{8} 9 + 2 x - (- 3 + x) d x

\int_{- \frac{9}{2}}^{0} 9 + 2 x - (- 9 + 2 x) d x = 18

\int_{0}^{8} 9 + 2 x - (- 3 + x) d x = \frac{74}{3}

= 18 + \frac{74}{3}

Simplify

= \frac{128}{3}

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Frequently Asked Questions (FAQ)

What is area y^2-2x=9,x-y=3 ?
The answer to area y^2-2x=9,x-y=3 is 128/3