What is the average distance between a point in the

sebadillab0 2022-07-12 Answered
What is the average distance between a point in the interval [-4,3] and the origin?
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Answers (1)

treccinair
Answered 2022-07-13 Author has 18 answers
The distance between a point x on the number line and the origin is |x|
We have been asked for the average value of this function on the interval [-4, 3]
We can either evaluate 1 3 ( 4 ) 4 3 | x | d x or work through the equivalent geometry without the integral.
The area under graph of |x| and above [=4,3] consists of two isosceles right triangles.
On the left we have a triangle with base and height 4, so its area is 8.
On the right we have a triangle with base and height 3, so its area is 9 2
The total area under the graph is 25 2
Divide by the total base of 3+4=7 to get an average value of 25 14
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