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Popular >

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

Solution

area

y = 2 - \frac{x}{2}, x = 2 y^{2}

Solution

9

Solution steps

Isolate

y

for

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

f_{1} (x) = 2 - \frac{x}{2}

f_{2} (x) = \frac{x}{2}

To find the intersection points solve

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

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

2 - \frac{x}{2} = - \frac{x}{2} : x = 8

\frac{x}{2} = - \frac{x}{2} : x = 0

= \int_{0}^{2} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{2}^{8} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{0}^{2} \frac{x}{2} - (- \frac{x}{2}) d x + \int_{2}^{8} 2 - \frac{x}{2} - (- \frac{x}{2}) d x

\int_{0}^{2} \frac{x}{2} - (- \frac{x}{2}) d x = \frac{8}{3}

\int_{2}^{8} 2 - \frac{x}{2} - (- \frac{x}{2}) d x = \frac{19}{3}

= \frac{8}{3} + \frac{19}{3}

Simplify

= 9

Popular Examples

integral of (9x+2)^2

\int (9 x + 2)^{2} d x

integral of (a+bx^5)/(6ax+bx^6)

\int \frac{a + b x ^{5}}{6 a x + b x ^{6}} d x

y^{''}+4y^'-24y=0

y^{^{''}} + 4 y^{^{'}} - 24 y = 0

integral of e^x+e^xx

\int e^{x} + e^{x} x d x

derivative of g(x)= 1/(sqrt(x))derivative of

g (x) = \frac{1}{x}

Frequently Asked Questions (FAQ)

What is area y=2-x/2 ,x=2y^2 ?
The answer to area y=2-x/2 ,x=2y^2 is 9