• Support PF! Buy your school textbooks, materials and every day products Here!

Setup an integral for the curve

  • #1

Homework Statement


for the curve x= sqrt(64-y^2), -4<=y<=4

(identify from multiple choice
1. setup an integral for the curve.
2. identify the graph
3. find the length of the curve.


Homework Equations


x = sqrt(64-y^2), -4<=y<=4


The Attempt at a Solution


1. dx/dy = y*sqrt(64-y^2)
2. (dx/dy)^2 = y^2 * (64-y^2)
3. integral (-4 to 4) sqrt(1 + 64y^2 - y^4)

1. however, the answer for integral for the length is
L=Integral(-4,4) 8(64-y^2)^(-1/2) dy. i'm not sure how they got that?

2. i'm not sure how to graph this function.
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
251
hi whatlifeform! :smile:
x = sqrt(64-y^2), -4<=y<=4

1. dx/dy = y*sqrt(64-y^2)
no, you've correctly got the 2y and the 1/2,

but you haven't differentiated the function: the √ should become 1/2 1/√ :wink:

(generally, ()n in the chain rule becomes n()n-1)
 
  • #3
hi whatlifeform! :smile:


no, you've correctly got the 2y and the 1/2,

but you haven't differentiated the function: the √ should become 1/2 1/√ :wink:

(generally, ()n in the chain rule becomes n()n-1)
what do you mean?
 
  • #4
i've got L = integral (-4,4) sqrt (1 + (y^2)/(64-y^2)) dy

however, i'm not sure how to get to: L=Integral(-4,4) 8(64-y^2)^(-1/2) dy
 
  • #5
update: got it solved. but i'm still not sure how to graph this function.
 
  • #6
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
33,529
5,450
update: got it solved. but i'm still not sure how to graph this function.
What do you get if you square both sides to get rid of the square root? Do you recognise the form that results?
 
  • #7
tiny-tim
Science Advisor
Homework Helper
25,832
251
ie, what is x2 = 64 - y2 ? :smile:
 
  • #9
dx
Homework Helper
Gold Member
2,011
18
x2 + y2 = a2

is an origin-centered circle with radius a
 

Related Threads on Setup an integral for the curve

  • Last Post
Replies
1
Views
798
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
11
Views
1K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
5
Views
712
Replies
7
Views
18K
Replies
3
Views
2K
Replies
1
Views
442
  • Last Post
Replies
2
Views
2K
Top