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Popular Calculus >

area x+y=7,x+5=y^2

Solution

area

x + y = 7, x + 5 = y^{2}

Solution

\frac{343}{6}

+1

Decimal

57.16666 \dots

Solution steps

Isolate

y

for

x + y = 7 : y = 7 - x

Isolate

y

for

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

f_{1} (x) = 7 - x

f_{2} (x) = x + 5

To find the intersection points solve

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

7 - x = x + 5 : x = 4

7 - x = - x + 5 : x = 11

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

= \int_{- 5}^{4} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{4}^{11} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 5}^{4} x + 5 - (- x + 5) d x + \int_{4}^{11} 7 - x - (- x + 5) d x

\int_{- 5}^{4} x + 5 - (- x + 5) d x = 36

\int_{4}^{11} 7 - x - (- x + 5) d x = \frac{127}{6}

= 36 + \frac{127}{6}

Simplify

= \frac{343}{6}

Graph

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Frequently Asked Questions (FAQ)

What is area x+y=7,x+5=y^2 ?
The answer to area x+y=7,x+5=y^2 is 343/6