What is area x,4x,-x+2 ?

The answer to area x,4x,-x+2 is 3/5

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area x,4x,-x+2

area

x, 4 x, - x + 2

\frac{3}{5}

Decimal Notation

0.6

Solution steps

To find the intersection points solve

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

x = 4 x : x = 0

x = - x + 2 : x = 1

4 x = - x + 2 : x = \frac{2}{5}

= \int_{0}^{\frac{2}{5}} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{\frac{2}{5}}^{1} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{0}^{\frac{2}{5}} ∣ x - 4 x ∣ d x + \int_{\frac{2}{5}}^{1} ∣ x - (- x + 2) ∣ d x

\int_{0}^{\frac{2}{5}} ∣ x - 4 x ∣ d x = \frac{6}{25}

\int_{\frac{2}{5}}^{1} ∣ x - (- x + 2) ∣ d x = \frac{9}{25}

= \frac{6}{25} + \frac{9}{25}

Simplify

= \frac{3}{5}

\int \frac{1}{25 + 9 x ^{2}} d x

\frac{\partial}{\partial x} (3 ln (x^{2} + y^{2}))

\frac{d}{d x} (sin (- 1 (2 x + 1)))

\int - sec^{2} (\frac{3 x}{2}) d x

\frac{d}{d x} (\frac{ln ( 2 x )}{x})