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Popular >

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

Solution

area

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

Solution

2

Solution steps

Isolate

y

for

x + y = 4 : y = 4 - x

f_{1} (x) = x

f_{2} (x) = 3 x

To find the intersection points solve

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

x = 3 x : x = 0

x = 4 - x : x = 2

3 x = 4 - x : 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 - (4 - x) ∣ d x

\int_{0}^{1} ∣ x - 3 x ∣ d x = 1

\int_{1}^{2} ∣ x - (4 - x) ∣ d x = 1

= 1 + 1

Simplify

= 2

Graph

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Frequently Asked Questions (FAQ)

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