Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
(a) Graph the curve $ y = x \sqrt[3]{4 - x} $ , $ 0 \le x \le 4 $.(b) Compute the lengths of inscribed polygons with $ n = 1 $, 2, and 4 sides. (Divide the interval into equal sub-intervals.) Illustrate by sketching these polygons (as in Figure 6).(c) Set up an integral for the length of the curve.(d) Use your calculator to find the length of the curve to four decimal places. Compare with the approximations in part (b).
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Clarissa Noh
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
Calculus 2 / BC
Chapter 8
Further Applications of Integration
Section 1
Arc Length
Applications of Integration
Missouri State University
Campbell University
Oregon State University
Idaho State University
Lectures
14:15
$\begin{array}{l}{\text { …
01:02
(a) Graph the curve $y=x \…
16:11
02:19
Estimate the length of the…
01:07
01:03
02:00
02:24
02:32
02:12
01:04
02:18
Graph the curve and visual…
02:51
he has clear. So when you read here, so for part, they already drew the graph. So it looks something like this to curve for part B. We're gonna find the link, so you know that the bottom is for so from zero half of zero and four comma effort for building this For now, if we look it this polygon from zero comma zero, 22 comma F comma too. We see that feeling is going to be so from 00 comma zero two comma F comma till it gives us two comma too Que brute go to and of for comma zero. So the length is approximately 6.43 And finally the length for the 0.0 comma zero one comma Q Bert of three to Comack, You brute Too common to cube root of two three com a three and four comma zero The length is approximately 7.5 for part C. We're gonna find the arc length equation So we have our why is equal to x cuba it of four minus x. So are derivative. Gives us 12 minus four x over three arms form minus X to the 2/3 power. So l is equal to from 0 to 4 square root of one plus 12 minus for X over three times four minus X to the 2/3 power. And we square this the ex finally, for party. We're just gonna need a calculator and we get approximately 7.79 879 here, in part being we found the length of the curve using polygons, and we see that these are all under estimates. So we conclude that the actual value is larger since for our approximations, we're using it were using straight lines.
View More Answers From This Book
Find Another Textbook
01:13
Consultant for an association of personal directors wants to find out what p…
A telephone switch board in a firm receives on a average 90 calls per hour. …
01:43
A study by a University found that one in five 13- and 14-year-olds is a som…
04:44
A doctor is considering prescribing a new medication that helps lower blood …
02:03
The mean weight from a sample of 256 computer parts created by a computer ma…
02:58
In Connecticut, auto license plates carry 3 digits followed by 3 letters. (A…
03:26
An ordinary deck of playing cards contains 52 cards, 26 red and 26 black. If…
00:37
researcher is interested in whether a new reading technique influences the …
04:53
> set.seed(1234)> ind <- sample(2, nrow(iris), replace=TRUE…
01:57
Average weight of newborn babies is bell-shaped with mean of 3325 grams …
