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Popular Calculus >

area x=y^2,x=y+6

Solution

area

x = y^{2}, x = y + 6

Solution

\frac{125}{6}

+1

Decimal

20.83333 \dots

Solution steps

Isolate

y

for

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

Isolate

y

for

x = y + 6 : y = x - 6

f_{1} (x) = x

f_{2} (x) = - x

To find the intersection points solve

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

x = - x : x = 0

x = x - 6 : x = 9

- x = x - 6 : x = 4

= \int_{0}^{4} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{4}^{9} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{0}^{4} x - (- x) d x + \int_{4}^{9} x - (x - 6) d x

\int_{0}^{4} x - (- x) d x = \frac{32}{3}

\int_{4}^{9} x - (x - 6) d x = \frac{61}{6}

= \frac{32}{3} + \frac{61}{6}

Simplify

= \frac{125}{6}

Graph

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Frequently Asked Questions (FAQ)

What is area x=y^2,x=y+6 ?
The answer to area x=y^2,x=y+6 is 125/6