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
The centroid of a $ curve $ can be found by a process similar to the one we used for finding the centroid of a region. If $ C $ is a curve with length $ L $, then the centroid is $ (\bar{x}, \bar{y}) $ where $ \bar{x} = (\frac{1}{L}) \int x\ ds $ and $ \bar{y} = (\frac{1}{L}) \int y\ ds $. Here we assign appropriate limits of integration, and $ ds $ is as defined in Sections 8.1 and 8.2. ( The centroid often doesn't lie on the curve itself. If the curve were made of wire and placed on a weightless board, the centroid would be the balance point on the board.) Find the centroid of the quarter-circle $ y = \sqrt{16 - x^2} $, $ 0 \le x \le 4 $.
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Doruk Isik
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 3
Applications to Physics and Engineering
Applications of Integration
Oregon State University
Harvey Mudd College
Baylor University
Boston College
Lectures
01:09
The centroid of a curve ca…
03:44
The centroid of curve can …
01:39
Let $\mathscr{R}$ be the r…
01:05
Let $C$ be a simple curve …
Let $\mathscr{H}$ be the r…
04:31
Most centroid calculations…
10:10
03:29
Centroid of unbounded regi…
Hey, miss problem. We're giving any question of any 1/4 for circle. Why? Didn't give any question is why's it called scourge sexy sex card. If he noted exchanges between 04 and thes e questions are also known and given in a problem statement, we're trying to come play export and white bar for a 1/4 off a circle. All right, since we're going to use be given equations, we first need to calculate D s. And this is our be calculated in order Chocolate D s. We would need to first find the thereto. Ought to give any question which respect him. Thanks. So let's tag narrative off. Why would suspect Activity X would be won over Skirt one over to skirted of 16 lines, expiry months. Bye bye. There was intervention. It's native to X Tuesday against love. So we have that one has negative X delight. I'm skirted of 16 months excrement and skirt of that S O D I D X skirt would done be equal to X squared. Divided by 16 months. Ex skirt. All right, we have everything we need. Less display goes in. Export is equal to one over l what is L l in this case is the circumference. And for a circle circumference is two point times radius. And as you can see, Radius s four side will be to buy times for I've ever given 1/4 of the circles of in to divide this spot for So does your conference off that peace will only be two ply or s o for expert. We have won over length one or two by integral forms here before x times d s where d s is scribbled off one plus thes y d X skirt that is equal to x Great delight by 16 lines Expert The X that is equal to one over to pie trickle from 0 to 4 X times skirt of 16 divided by a skirt of 16 months Ex crime DX How did I get this Second port? Well, all I did was to multiplied this, uh, one by 16 minus explorer. And do I buy the same number? Skirted off 16 is equal to four. And we can just take this one outside the in. Jekyll and right export as, um four over to pie. Internal dessert for ex skirted off 16 months Ex card here, We're going to say that 16 months Next. Carter's our new variable. You saw that native to X E X would be to you and X t x Could dummy continue native d'you or two? And since dishonorable one X is zero you 16 and one access for you. The zeroes are the limits of formula In title will be then from 16 too zero he have negative d'you deal. I skirted a few soling Thus we find expert to be equal to eight or pie LSD chocolate white bar Why bar is worn over el again one over to buy integrate forms here to walk For this time we're gonna let's buy Why buy deep s we know what dances and we know why as a function of X status given to us So that'll be 16 months Ex crane multiplied by, uh skirted up d s, which is this part in which we calculated it to be as this term. So that would be skirted of 16. Delighted by skirted off 16 minus expert the ex Nazis will cancel out skirted off 16. It's four. So we have four over to pie off ex were exchanged between 04 That is an equal to 16 over to pie, which is eight or apply. So from this, we can export to be equal to eight over five. Why part to be equal to eight over pi.
View More Answers From This Book
Find Another Textbook
01:59
"Graph a right triangle with the two points forming the hypotenuse. Usi…
02:38
'Describe the given sets with a single equation or pair of equations Th…
01:24
'Evaluate the limit; If It exists. (If an answer does not exist, enter …
02:20
'A function is given f(t) 4t2; t= 3,t = 3 + h(a) Determine the net …
01:46
'least one of the answers above is NOT correct point) This problem …
02:39
'The amount of mustard dispensed from machine at The Hotdog Emporium is…
01:06
'72) Find the z-score for the value 55, when the mean is 58 and the sta…
01:49
"Challenge Question: A cylinder [s three times as high #s It Is wldes T…
02:53
'polntz SCalcET8 2 5 043Find each X-value at which fis discontinu…
03:58
'47 (a) Draw all trees of order 5. (b) Draw all forests of order 6.…