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Kellystar27
06.08.2019 •
Mathematics
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.
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Ответ:
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
Ответ:
Step-by-step explanation: