Use the arc length formula to find the length of the curve y = 5x − 1, −3 ≤ x ≤ 2. check your answer by noting that the curve is a line segment and calculating its length by the distance formula.

  length = 5√26

Step-by-step explanation:

The arc length of f(x) on the interval [a, b] is given by ...

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 ...

_____

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

7 ft 6 in means 7 1/2, because 6 in is 1/2 of a foot. 7 ft 8 in means 7 2/3 because 8 in is 2/3 of a foot. 23/3 = 7 2/3. 15/2 = 7 1/2.

23/3   *   15/2   = 57 1/2

step-by-step explanation: