# Setup an integral for the curve

## 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.

tiny-tim
Homework Helper
hi whatlifeform!
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/√

(generally, ()n in the chain rule becomes n()n-1)

hi whatlifeform!

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

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

(generally, ()n in the chain rule becomes n()n-1)
what do you mean?

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

update: got it solved. but i'm still not sure how to graph this function.

haruspex
Homework Helper
Gold Member
2020 Award
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?

tiny-tim
Homework Helper
ie, what is x2 = 64 - y2 ?

ie, what is x2 = 64 - y2 ?

the graph of?

dx
Homework Helper
Gold Member
x2 + y2 = a2

is an origin-centered circle with radius a