How do we explain the Riemann sum process that leads to the definite integral that computes arc length?

Step-by-step explanation:

Consider two points on a curve, (xᵢ, yᵢ) and (xᵢ₊₁, yᵢ₊₁).  The distance between them can be found with distance formula:

d = √((xᵢ₊₁ − xᵢ)² + (yᵢ₊₁ − yᵢ)²)

d = √((Δx)² + (Δy)²)

Factor out Δx:

d = √(1 + (Δy/Δx)²) Δx

Adding up the distances from i=1 to i=n, the total arc length can be approximated as:

s ≈ ∑ᵢ₌₁ⁿ √(1 + (Δy/Δx)²) Δx

Taking the limit as n approaches infinity, we get the exact value of s:

s = lim(n→∞) ∑ᵢ₌₁ⁿ √(1 + (Δy/Δx)²) Δx

Which can be written as a definite integral:

s = ∫ₐᵇ √(1 + (dy/dx)²) dx

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

the median is   36 orr sum like dat

step-by-step explanation: