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Popular >

area x+y=13,x+7=y^2

Solution

area

x + y = 13, x + 7 = y^{2}

Solution

\frac{243}{2}

+1

Decimal

121.5

Solution steps

Isolate

y

for

x + y = 13 : y = 13 - x

Isolate

y

for

x + 7 = y^{2} : y = x + 7, y = - x + 7

f_{1} (x) = 13 - x

f_{2} (x) = x + 7

To find the intersection points solve

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

13 - x = x + 7 : x = 9

13 - x = - x + 7 : x = 18

x + 7 = - x + 7 : x = - 7

= \int_{- 7}^{9} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{9}^{18} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 7}^{9} x + 7 - (- x + 7) d x + \int_{9}^{18} 13 - x - (- x + 7) d x

\int_{- 7}^{9} x + 7 - (- x + 7) d x = \frac{256}{3}

\int_{9}^{18} 13 - x - (- x + 7) d x = \frac{217}{6}

= \frac{256}{3} + \frac{217}{6}

Simplify

= \frac{243}{2}

Graph

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Frequently Asked Questions (FAQ)

What is area x+y=13,x+7=y^2 ?
The answer to area x+y=13,x+7=y^2 is 243/2