Question
:onsider the curve
for
. Find the arc length of the curve.
Ask by Gough Edwards. in the United States
Jan 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The arc length of the curve from
to
is
units.
Solution

Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.

Answered by UpStudy AI and reviewed by a Professional Tutor
Like
The Deep Dive
To find the arc length of the curve given by
from
to
, we can use the formula for the arc length of a curve defined as
:
-
First, we need to compute the derivative
: -
Next, square the derivative:
-
Now, we will use the arc length formula:Which simplifies to:This further simplifies to:
-
We can write:
Using the identity
, this way we can explore a simpler integral if possible.
- The final integral can be calculated either analytically or numerically over the evaluated limits from
to .
After solving, the arc length
evaluates to:
Eventually, computing all the terms will provide the arc length of the curve from
to
.
Therefore, the arc length, when calculated completely, is found to be: