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Popular >

area x+y^2=12,x+y=0

Solution

area

x + y^{2} = 12, x + y = 0

Solution

\frac{343}{6}

+1

Decimal Notation

57.16666 \dots

Solution steps

Isolate

y

for

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

Isolate

y

for

x + y = 0 : y = - x

f_{1} (x) = 12 - x

f_{2} (x) = - 12 - x

To find the intersection points solve

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

12 - x = - 12 - x : x = 12

12 - x = - x : x = - 4

- 12 - x = - x : x = 3

= \int_{- 4}^{3} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{3}^{12} ∣ f_{2} (x) - f_{1} (x) ∣ d x

= \int_{- 4}^{3} 12 - x - (- x) d x + \int_{3}^{12} - 12 - x - 12 - x d x

\int_{- 4}^{3} 12 - x - (- x) d x = \frac{127}{6}

\int_{3}^{12} - 12 - x - 12 - x d x = 36

= \frac{127}{6} + 36

Simplify

= \frac{343}{6}

Popular Examples

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\int tan^{5} (2 x) sec^{4} (2 x) d x

integral of 1/(sqrt(t^2-4t+29))

\int \frac{1}{t ^{2} - 4 t + 29} d t

integral of sqrt(4-t)

\int 4 - t d t

integral from 0 to 2 of (x^2-2)^4x

\int_{0}^{2} (x^{2} - 2)^{4} x d x

area y=4x,y= 5/4 x,y=21-x^2 area

y = 4 x, y = \frac{5}{4} x, y = 21 - x^{2}

Frequently Asked Questions (FAQ)

What is area x+y^2=12,x+y=0 ?
The answer to area x+y^2=12,x+y=0 is 343/6