the blue lake trail is 11 3/8 miles long. gemma has hiked 2 1/2 miles each hour for 3 hours. how far is she from the end?
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By using the arc length formula, we will see that the length of the curve is L = 1.48
<h3>How to use the arc length formula?</h3>
Here we have the curve:
y = 2 - x^2 with 0 ≤ x ≤ 1
And we want to find the length of the curve.
The arc length formula for a curve y in the interval [x₁, x₂] is given by:
For our curve, we have:
dy/dx = -2x
And the interval is [0, 1]
Replacing that we get:
This integral is not trivial, using a table you can see that this is equal to:
evaluated from x = 1 to x = 0, when we do that, we will get:
That is the length of the curve.
If you want to learn more about curve length, you can read: