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Popular >

area x-y^2=1,x+y=7

Solution

area

x - y^{2} = 1, x + y = 7

Solution

\frac{125}{6}

+1

Solution steps

Isolate

y

for

x - y^{2} = 1 : y = - 1 + x, y = - - 1 + x

Isolate

y

for

x + y = 7 : y = 7 - x

f_{1} (x) = - 1 + x

f_{2} (x) = - - 1 + x

To find the intersection points solve

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

- 1 + x = - - 1 + x : x = 1

- 1 + x = 7 - x : x = 5

- - 1 + x = 7 - x : x = 10

= \int_{1}^{5} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{5}^{10} ∣ f_{2} (x) - f_{3} (x) ∣ d x

= \int_{1}^{5} - 1 + x - (- - 1 + x) d x + \int_{5}^{10} - - 1 + x - (7 - x) d x

\int_{1}^{5} - 1 + x - (- - 1 + x) d x = \frac{32}{3}

\int_{5}^{10} - - 1 + x - (7 - x) d x = \frac{61}{6}

= \frac{32}{3} + \frac{61}{6}

Simplify

= \frac{125}{6}

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\frac{d}{d t} (ln (2 t + 1))

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\int \frac{1}{3 x + 1} d x

\int 64 d x

Frequently Asked Questions (FAQ)

What is area x-y^2=1,x+y=7 ?
The answer to area x-y^2=1,x+y=7 is 125/6