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Popular >

area y^2-2x=1,x-y=1

Solution

area

y^{2} - 2 x = 1, x - y = 1

Solution

\frac{16}{3}

+1

Decimal Notation

5.33333 \dots

Solution steps

Isolate

y

for

y^{2} - 2 x = 1 : y = 1 + 2 x, y = - 1 + 2 x

Isolate

y

for

x - y = 1 : y = - 1 + x

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

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

To find the intersection points solve

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

1 + 2 x = - 1 + 2 x : x = - \frac{1}{2}

1 + 2 x = - 1 + x : x = 4

- 1 + 2 x = - 1 + x : x = 0

= \int_{- \frac{1}{2}}^{0} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{0}^{4} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- \frac{1}{2}}^{0} 1 + 2 x - (- 1 + 2 x) d x + \int_{0}^{4} 1 + 2 x - (- 1 + x) d x

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

\int_{0}^{4} 1 + 2 x - (- 1 + x) d x = \frac{14}{3}

= \frac{2}{3} + \frac{14}{3}

Simplify

= \frac{16}{3}

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\int (10 x + 6) d x

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Frequently Asked Questions (FAQ)

What is area y^2-2x=1,x-y=1 ?
The answer to area y^2-2x=1,x-y=1 is 16/3