How do you find the arc length of the curve y = 2x - 3, -2 ≤ x ≤ 1?

1 Answer
Jun 26, 2015

The arc length is 3sqrt{5}\approx 6.7082

Explanation:

Since the graph of y=f(x)=2x-3 is a straight line, there's actually no need to use calculus. Instead, just find the straight-line distance between the points (-2,f(-2))=(-2,-7) and (1,f(1))=(1,-1). The answer, by the distance formula (Pythagorean theorem), is

sqrt{(-2-1)^2+(-7-(-1))^2}=sqrt{9+36}=sqrt{45}

=sqrt{9}sqrt{5}=3sqrt{5}\approx 6.7082

If you want to confirm this with calculus, evaluate the integral int_{-2}^{1}sqrt{1+(f'(x))^2}\ dx=int_{-2}^{1}sqrt{1+4}\ dx

=sqrt{5}x|_{-2}^{1}=sqrt{5}(1-(-2))=3sqrt{5}