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Example Questions
Example Question #1 : Arc Length And Curvature
Determine the length of the curve , on the interval
First we need to find the tangent vector, and find its magnitude.
Now we can set up our arc length integral
Example Question #2 : Arc Length And Curvature
Determine the length of the curve , on the interval
First we need to find the tangent vector, and find its magnitude.
Now we can set up our arc length integral
Example Question #3 : Arc Length And Curvature
Find the length of the curve , from
, to
None of the other answers
The formula for the length of a parametric curve in 3-dimensional space is
Taking dervatives and substituting, we have
. Factor a
out of the square root.
. "Uncancel" an
next to the
. Now there is a perfect square inside the square root.
. Factor
. Take the square root, and integrate.
Example Question #4 : Arc Length And Curvature
Find the length of the arc drawn out by the vector function with
from
to
.
None of the other answers
To find the arc length of a function, we use the formula
.
Using we have
Example Question #5 : Arc Length And Curvature
Evaluate the curvature of the function at the point
.
The formula for curvature of a Cartesian equation is . (It's not the easiest to remember, but it's the most convenient form for Cartesian equations.)
We have , hence
and .
Example Question #6 : Arc Length And Curvature
Find the length of the parametric curve
for .
To find the solution, we need to evaluate
.
First, we find
, which leads to
.
So we have a final expression to integrate for our answer
Example Question #7 : Arc Length And Curvature
Determine the length of the curve given below on the interval 0<t<2
The length of a curve r is given by:
To solve:
Example Question #8 : Arc Length And Curvature
Find the arc length of the curve
on the interval
To find the arc length of the curve function
on the interval
we follow the formula
For the curve function in this problem we have
and following the arc length formula we solve for the integral
Hence the arc length is
Example Question #601 : Calculus 3
Find the arc length of the curve function
On the interval
Round to the nearest tenth.
To find the arc length of the curve function
on the interval
we follow the formula
For the curve function in this problem we have
and following the arc length formula we solve for the integral
Using u-substitution, we have
and
The integral then becomes
Hence the arc length is
Example Question #1 : Arc Length And Curvature
Given that a curve is defined by , find the arc length in the interval
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