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Popular >

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

Solution

area

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

Solution

\frac{32}{3}

+1

Solution steps

Isolate

y

for

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

Isolate

y

for

x - 2 y = 3 : y = - \frac{3 - x}{2}

f_{1} (x) = x

f_{2} (x) = - x

To find the intersection points solve

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

x = - x : x = 0

x = - \frac{3 - x}{2} : x = 9

- x = - \frac{3 - x}{2} : x = 1

= \int_{0}^{1} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{1}^{9} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{0}^{1} x - (- x) d x + \int_{1}^{9} x - (- \frac{3 - x}{2}) d x

\int_{0}^{1} x - (- x) d x = \frac{4}{3}

\int_{1}^{9} x - (- \frac{3 - x}{2}) d x = \frac{28}{3}

= \frac{4}{3} + \frac{28}{3}

Simplify

= \frac{32}{3}

Popular Examples

derivative of 3x(x^2-x+1(5x-3))

\frac{d}{d x} (3 x (x^{2} - x + 1) (5 x - 3))

(dy)/(dt)=-2y,y(0)= 1/10

\frac{d y}{d t} = - 2 y, y (0) = \frac{1}{10}

tangent of x^2-8 tangent of

x^{2} - 8

derivative of sin(2xcos(2x))

\frac{d}{d x} (sin (2 x) cos (2 x))

tangent of f(x)=x^3,\at x=6 tangent of

f (x) = x^{3}, at x = 6

Frequently Asked Questions (FAQ)

What is area y^2=x,x-2y=3 ?
The answer to area y^2=x,x-2y=3 is 32/3