This tutorial discusses three ways to use Green's theorem to find the area of a hypocycloid by changing the parameterization to x=aθt and y=aθt, where 0≤t≤2. It recommends using the formula that involves both x and y, giving the equations dx=-3aθdt and dy=3aθdt to substitute into the Green's theorem area formula and solve the resulting integration.

1. FOR CLASS EN.MUGHTI
TUTORIAL 6, 16/4/2013
8. Find the volume of a hypocycloid + = by changing the
parameter to x = a t,y=a t,
0 t 2 .
Important: change volume to area.
Then, we can use GREEN THEOREM formula.
There are 3 ways to find area using GREEN THEOREM
1. Using x
2. Using y
3. Using both x and y.
For question 8, we will use formula that use both x and y.
NOW, using all the information given,
x=a t,y=a t,0 t 2 .
dx = -3 a ,
dy = 3 a ,
Substitute into the formula
A= ∫

2. A= ∫ (-3 a + (3 a
.
.
.
Then, solve this integration.
ANSWER:
=
GOOD LUCK…