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Popular Calculus >

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

Solution

area

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

Solution

\frac{9}{2}

+1

Decimal

4.5

Solution steps

Isolate

y

for

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

Isolate

y

for

y + x = 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 = 0

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

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

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

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

\int_{0}^{3} - x + 1 - (1 - x) d x = \frac{19}{6}

= \frac{4}{3} + \frac{19}{6}

Simplify

= \frac{9}{2}

Graph

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Frequently Asked Questions (FAQ)

What is area y^2=x+1,y+x=1 ?
The answer to area y^2=x+1,y+x=1 is 9/2