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Popular >

area y^2-3x=1,x-y=3

Solution

area

y^{2} - 3 x = 1, x - y = 3

Solution

\frac{343}{18}

+1

Decimal Notation

19.05555 \dots

Solution steps

Isolate

y

for

y^{2} - 3 x = 1 : y = 1 + 3 x, y = - 1 + 3 x

Isolate

y

for

x - y = 3 : y = - 3 + x

f_{1} (x) = 1 + 3 x

f_{2} (x) = - 1 + 3 x

To find the intersection points solve

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

1 + 3 x = - 1 + 3 x : x = - \frac{1}{3}

1 + 3 x = - 3 + x : x = 8

- 1 + 3 x = - 3 + x : x = 1

= \int_{- \frac{1}{3}}^{1} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{1}^{8} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- \frac{1}{3}}^{1} 1 + 3 x - (- 1 + 3 x) d x + \int_{1}^{8} 1 + 3 x - (- 3 + x) d x

\int_{- \frac{1}{3}}^{1} 1 + 3 x - (- 1 + 3 x) d x = \frac{32}{9}

\int_{1}^{8} 1 + 3 x - (- 3 + x) d x = \frac{31}{2}

= \frac{32}{9} + \frac{31}{2}

Simplify

= \frac{343}{18}

Popular Examples

(dy)/(dt)=-100y+101cos(t)+99sin(t)

\frac{d y}{d t} = - 100 y + 101 cos (t) + 99 sin (t)

tangent of y=2e^x-3x+1,\at x=0 tangent of

y = 2 e^{x} - 3 x + 1, at x = 0

derivative of 4x^2-12x+5 derivative of

4 x^{2} - 12 x + 5

integral of-2x^2sin(pix)

\int - 2 x^{2} sin (π x) d x

integral of y/y

\int \frac{y}{y} d y

Frequently Asked Questions (FAQ)

What is area y^2-3x=1,x-y=3 ?
The answer to area y^2-3x=1,x-y=3 is 343/18