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Popular >

area y^2=2x,y=-4+x

Solution

area

y^{2} = 2 x, y = - 4 + x

Solution

18

Solution steps

Isolate

y

for

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

f_{1} (x) = 2 x

f_{2} (x) = - 2 x

To find the intersection points solve

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

2 x = - 2 x : x = 0

2 x = - 4 + x : x = 8

- 2 x = - 4 + x : x = 2

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

= \int_{0}^{2} 2 x - (- 2 x) d x + \int_{2}^{8} 2 x - (- 4 + x) d x

\int_{0}^{2} 2 x - (- 2 x) d x = \frac{16}{3}

\int_{2}^{8} 2 x - (- 4 + x) d x = \frac{38}{3}

= \frac{16}{3} + \frac{38}{3}

Simplify

= 18

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\int \frac{1}{25 - 4 x ^{2}} d x

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\int t \cdot cos (t) d t

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\int 18 sin^{3} (x) cos^{2} (x) d x

y^{''}+4y^'+5y=-10x+e^{-x}

y^{^{''}} + 4 y^{^{'}} + 5 y = - 10 x + e^{- x}

laplacetransform te^{2t}sin(6t)laplace transform

t e^{2 t} sin (6 t)

Frequently Asked Questions (FAQ)

What is area y^2=2x,y=-4+x ?
The answer to area y^2=2x,y=-4+x is 18