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Popular >

area y=x,y=3x,y=-x+4

Solution

area

y = x, y = 3 x, y = - x + 4

Solution

2

Solution steps

To find the intersection points solve

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

x = 3 x : x = 0

x = - x + 4 : x = 2

3 x = - x + 4 : x = 1

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

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

\int_{0}^{1} ∣ x - 3 x ∣ d x = 1

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

= 1 + 1

Simplify

= 2

Graph

Popular Examples

(y+sqrt(xy))dx=xdy

(y + x y) d x = x d y

(\partial)/(\partial x)(sqrt((2x)/(x^2+1)))

\frac{\partial}{\partial x} (\frac{2 x}{x ^{2} + 1})

tangent of 12x^2+3x tangent of

12 x^{2} + 3 x

f (x) = 4 - 5 x^{2}

limit as x approaches a of sqrt(x-a)+c

x \to a lim (x - a + c)

Frequently Asked Questions (FAQ)

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