Answer:
length = 5√26
Step-by-step explanation:
The arc length of f(x) on the interval [a, b] is given by ...
[tex]\displaystyle d=\int\limits_a^b{\sqrt{1+f'(x)^2}}\,dx[/tex]
In the present case, we have ...
f(x) = 5x -1
f'(x) = 5
on the interval [a, b] = [-3, 2]. Then the arc length is ...
[tex]\displaystyle d=\int\limits_{-3}^2{\sqrt{1+5^2}}\,dx=\sqrt{26}(2-(-3))\\\\d=5\sqrt{26}[/tex]
_____
Check
We're looking for the distance between the points ...
(-3, f(-3)) = (-3, -16)
and
(2, f(2)) = (2, 9)
Using the distance formula, the distance is ...
d = √((2-(-3))² +(9-(-16))²) = √(5² +25²) = 5√(1+5²)
d = 5√26 . . . . . matches the integral result
