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Popular >

area x+y^2=42,x+y=0

Solution

area

x + y^{2} = 42, x + y = 0

Solution

\frac{2197}{6}

+1

Decimal Notation

366.16666 \dots

Solution steps

Isolate

y

for

x + y^{2} = 42 : y = 42 - x, y = - 42 - x

Isolate

y

for

x + y = 0 : y = - x

f_{1} (x) = 42 - x

f_{2} (x) = - 42 - x

To find the intersection points solve

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

42 - x = - 42 - x : x = 42

42 - x = - x : x = - 7

- 42 - x = - x : x = 6

= \int_{- 7}^{6} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{6}^{42} ∣ f_{2} (x) - f_{1} (x) ∣ d x

= \int_{- 7}^{6} 42 - x - (- x) d x + \int_{6}^{42} - 42 - x - 42 - x d x

\int_{- 7}^{6} 42 - x - (- x) d x = \frac{469}{6}

\int_{6}^{42} - 42 - x - 42 - x d x = 288

= \frac{469}{6} + 288

Simplify

= \frac{2197}{6}

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Frequently Asked Questions (FAQ)

What is area x+y^2=42,x+y=0 ?
The answer to area x+y^2=42,x+y=0 is 2197/6