What is the length of the path along the graph

Question

What is the length of the path along the graph of  between x = 2 and x = 4? (4 points)

answer choices

Answer 1

The answer is 4π/3.

Recognize that it is the graph of a half-circle of radius r = 4.

(It will help to draw the picture.)

You want to measure the length of its arc from its intersect with the x-axis to the point x = 2.

We just need to calculate the size of the angle α between the x-axis

and the line from the origin to the point (2, sqrt(r² - x²)).

Then the answer is then rα, provided α is expressed in radians.

We can calculate the angle α from

cos(α) = x/r = 2/4 = 0.5

Therefore

α = pi/3