Like
Report
Numerade Educator
Problem 9 Easy Difficulty
Find the exact length of the curve.
$ y = 1 + 6x^{\frac{3}{2}} $ , $ 0 \le x \le 1 $
Answer
$\frac{2}{243}(82 \sqrt{82}-1)$
Topics
Applications of Integration
Discussion
You must be signed in to discuss.
Top Calculus 2 / BC Educators
Catherine R.
Missouri State University
Anna Marie V.
Campbell University
Caleb E.
Baylor University
Joseph L.
Boston College
Watch More Solved Questions in Chapter 8
Video Transcript
Hey, it's Claire. So when you right here. So we have. Why is equal to one plus six x to the three hounds. When we differentiate this, we get d Y over D. X is equal to nine x to the one, huh? And using the art length formula we get l is equal to from 0 to 1 square e one plus nine x the 1/2 square d x this is equal to from 0 to 1 square root of one plus 81 x e x. We're gonna let you be equal to one plus 81 x So do you is equal to 81 d x. So this gives us well is equal to one over 81. And here we're gonna change the limits of integration. So a is equal to 82 and B is equal to one. So we put one 82 square root of you and then this gives us to over 243 Time 82 spirit of 82 minus one
Topics
Applications of Integration
Top Calculus 2 / BC Educators
Catherine R.
Missouri State University
Anna Marie V.
Campbell University
Caleb E.
Baylor University
Joseph L.
Boston College