What is area sqrt(x),y=x-2,y=0 ?

The answer to area sqrt(x),y=x-2,y=0 is 10/3

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area sqrt(x),y=x-2,y=0

area

x, y = x - 2, y = 0

\frac{10}{3}

Decimal Notation

3.33333 \dots

Solution steps

To find the intersection points solve

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

x - 2 = 0 : x = 2

x - 2 = x : x = 4

0 = x : x = 0

= \int_{0}^{2} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{2}^{4} ∣ f_{1} (x) - f_{3} (x) ∣ d x

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

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

\int_{2}^{4} x - 2 - x d x = \frac{16 - 4 2}{3} - 2

= \frac{4 2}{3} + \frac{16 - 4 2}{3} - 2

Simplify

= \frac{10}{3}

x \to 4 lim (ln (e^{x}))

x \to 0 lim (sin (1 x))

n = 1 \sum \infty e^{- n}

\frac{d}{d x} (\frac{1}{x ^{4} \cdot ( 5 - x )})

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