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Popular >

area x=6y^2,x+y=5

Solution

area

x = 6 y^{2}, x + y = 5

Solution

\frac{1331}{216}

+1

Decimal Notation

6.16203 \dots

Solution steps

Isolate

y

for

x = 6 y^{2} : y = \frac{x}{6}, y = - \frac{x}{6}

Isolate

y

for

x + y = 5 : y = 5 - x

f_{1} (x) = \frac{x}{6}

f_{2} (x) = - \frac{x}{6}

To find the intersection points solve

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

\frac{x}{6} = - \frac{x}{6} : x = 0

\frac{x}{6} = 5 - x : x = \frac{25}{6}

- \frac{x}{6} = 5 - x : x = 6

= \int_{0}^{\frac{25}{6}} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{\frac{25}{6}}^{6} ∣ f_{2} (x) - f_{3} (x) ∣ d x

= \int_{0}^{\frac{25}{6}} \frac{x}{6} - (- \frac{x}{6}) d x + \int_{\frac{25}{6}}^{6} - \frac{x}{6} - (5 - x) d x

\int_{0}^{\frac{25}{6}} \frac{x}{6} - (- \frac{x}{6}) d x = \frac{125}{27}

\int_{\frac{25}{6}}^{6} - \frac{x}{6} - (5 - x) d x = \frac{331}{216}

= \frac{125}{27} + \frac{331}{216}

Simplify

= \frac{1331}{216}

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Frequently Asked Questions (FAQ)

What is area x=6y^2,x+y=5 ?
The answer to area x=6y^2,x+y=5 is 1331/216