What is the average distance between a point in the

sebadillab0

sebadillab0

Answered question

2022-07-12

What is the average distance between a point in the interval [-4,3] and the origin?

Answer & Explanation

treccinair

treccinair

Beginner2022-07-13Added 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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