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Popular >

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

Solution

area

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

Solution

\frac{1}{6}

+1

Decimal

0.16666 \dots

Solution steps

Isolate

y

for

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

Isolate

y

for

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

f_{1} (x) = x - 1

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

To find the intersection points solve

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

x - 1 = - x - 1 : x = 1

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

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

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

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

\int_{1}^{2} x - 1 - (- 1 + x) d x = \frac{1}{6}

= \frac{1}{6}

Graph

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Frequently Asked Questions (FAQ)

What is area x=y^2+1,x-y=1 ?
The answer to area x=y^2+1,x-y=1 is 1/6