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Popular >

area y=x,y= x/3 ,y=2

Solution

area

y = x, y = \frac{x}{3}, y = 2

Solution

4

Solution steps

To find the intersection points solve

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

x = \frac{x}{3} : x = 0

x = 2 : x = 2

\frac{x}{3} = 2 : x = 6

= \int_{0}^{2} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{2}^{6} ∣ f_{2} (x) - f_{3} (x) ∣ d x

= \int_{0}^{2} x - \frac{x}{3} d x + \int_{2}^{6} \frac{x}{3} - 2 d x

\int_{0}^{2} x - \frac{x}{3} d x = \frac{4}{3}

\int_{2}^{6} \frac{x}{3} - 2 d x = \frac{8}{3}

= \frac{4}{3} + \frac{8}{3}

Simplify

= 4

Popular Examples

integral from 0 to 2 of x^2sqrt(1+x^3)

\int_{0}^{2} x^{2} 1 + x^{3} d x

derivative of 2/(1+4x^2)

\frac{d}{d x} (\frac{2}{1 + 4 x ^{2}})

integral of (x^2)/(sqrt(36+x^2))

\int \frac{x ^{2}}{36 + x ^{2}} d x

derivative of x^3-5 derivative of

x^{3} - 5

inverse oflaplace (3s-1)/(s^2-1)inverse laplace

\frac{3 s - 1}{s ^{2} - 1}

Frequently Asked Questions (FAQ)

What is area y=x,y= x/3 ,y=2 ?
The answer to area y=x,y= x/3 ,y=2 is 4