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Popular >

area x+3y=35,x+5=y^2

Solution

area

x + 3 y = 35, x + 5 = y^{2}

Solution

\frac{2197}{6}

+1

Decimal

366.16666 \dots

Solution steps

Isolate

y

for

x + 3 y = 35 : y = \frac{35 - x}{3}

Isolate

y

for

x + 5 = y^{2} : y = x + 5, y = - x + 5

f_{1} (x) = \frac{35 - x}{3}

f_{2} (x) = x + 5

To find the intersection points solve

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

\frac{35 - x}{3} = x + 5 : x = 20

\frac{35 - x}{3} = - x + 5 : x = 59

x + 5 = - x + 5 : x = - 5

= \int_{- 5}^{20} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{20}^{59} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 5}^{20} x + 5 - (- x + 5) d x + \int_{20}^{59} \frac{35 - x}{3} - (- x + 5) d x

\int_{- 5}^{20} x + 5 - (- x + 5) d x = \frac{500}{3}

\int_{20}^{59} \frac{35 - x}{3} - (- x + 5) d x = \frac{399}{2}

= \frac{500}{3} + \frac{399}{2}

Simplify

= \frac{2197}{6}

Graph

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Frequently Asked Questions (FAQ)

What is area x+3y=35,x+5=y^2 ?
The answer to area x+3y=35,x+5=y^2 is 2197/6