What is the general equation for the arclength of a line?
2 Answers
If we wish to find the arc length of
Explanation:
The general equation of a line is
Recall the formula for arc length is
The derivative of the linear function is
A = int_a^b sqrt(1 + m^2)dx
A = [sqrt(1+ m^2)x]_a^b
A = bsqrt(1 + m^2) - asqrt(1 + m^2)
A = (b - a)sqrt(1 + m^2)
Now let's verify to see if our formula is correct. Let
A = (6 - 2)sqrt(1 + 2^2) = 4sqrt(5)
If we were to use pythagoras, by connecting a horizontal line to a vertical line, we would get the following"
y(2) = 5
y(6) = 13
Delta y = 13 - 5 = 8
Delta x = 4
Thus
A = sqrt(80) = sqrt(16 * 5) = 4sqrt(5)
As obtained using our formula.
Hopefully this helps!
Explanation:
For the arc length of a linear function given its slope
Let
This may look scary because of all of the variables, but
The antiderivative is