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Popular >

area x=y+12,x=y^2+2y

Solution

area

x = y + 12, x = y^{2} + 2 y

Solution

\frac{343}{6}

+1

Decimal

57.16666 \dots

Solution steps

Isolate

y

for

x = y + 12 : y = x - 12

Isolate

y

for

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

f_{1} (x) = x - 12

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

To find the intersection points solve

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

x - 12 = - 1 + x + 1 : x = 15

x - 12 = - x + 1 - 1 : x = 8

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

= \int_{- 1}^{8} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{8}^{15} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{- 1}^{8} - 1 + x + 1 - (- x + 1 - 1) d x + \int_{8}^{15} x - 12 - (- 1 + x + 1) d x

\int_{- 1}^{8} - 1 + x + 1 - (- x + 1 - 1) d x = 36

\int_{8}^{15} x - 12 - (- 1 + x + 1) d x = \frac{127}{6}

= 36 + \frac{127}{6}

Simplify

= \frac{343}{6}

Graph

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Frequently Asked Questions (FAQ)

What is area x=y+12,x=y^2+2y ?
The answer to area x=y+12,x=y^2+2y is 343/6