What is the arclength of f ( x ) = x <mrow class="MJX-TeXAtom-ORD"> 5

Zion Wheeler

Zion Wheeler

Answered question

2022-06-10

What is the arclength of f ( x ) = x 5 x 4 + x in the interval [0,1]?

Answer & Explanation

lorienoldf7

lorienoldf7

Beginner2022-06-11Added 19 answers

The arc length of the function f(x) on the interval [a,b] can be found through:
s = a b 1 + ( f ( x ) ) 2 d x
So, here, we see that since f ( x ) = x 5 x 4 + x, we know that
f ( x ) = 5 x 4 4 x 3 + 1. Thus the arc length is equal to
s = 0 1 1 + ( 5 x 4 4 x 3 + 1 ) 2 d x
This can't be integrated by hand, so stick it into a calculator to see that
s 1.42326

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?