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Popular Calculus >

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

Solution

area

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

Solution

\frac{2197}{6}

+1

Decimal

366.16666 \dots

Solution steps

Isolate

y

for

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

Isolate

y

for

x = y : 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 = 6

- 42 - x = x : x = - 7

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

Graph

Popular Examples

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\int_{0}^{\frac{π}{8}} x (sec (2 x))^{2} d x

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\int arctan (9 t) d t

y^{^{'}} = - 2 y

integral of (2x-4)(x^2-4x+3)^5

\int (2 x - 4) (x^{2} - 4 x + 3)^{5} d x

2 t y^{^{'}} + 4 y = 3

Frequently Asked Questions (FAQ)

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