# Math Help - Area and Parametric Equations

1. ## Area and Parametric Equations

I have a question that I am working on and am having difficulties with part B finding the area. It looks like this:

The following parametric equations trace out a loop.
x = 6 - (5/2)t^2
y = (-5/6)t^3+5t+1

A)Find the t values at which the curve intersects itself:
t= +/- ______
b) What is the total area inside the loop?

For A my values are t= +/- Sqrt(6)

For the Area I had this
The integral from sqrt(6) to -Sqrt(6) = (25/6)t^4-25t^2-5t
When integrated = (25/6)(t^5/5)-25(t^3/3)-5(t^2/2) evaluated at sqrt(6) and (-sqrt6) this yeilds a negative answer and is not correct. CAN ANYONE HELP??

2. ## Green's Theorem

If C is a positively oreinted simple closed curve then the area enclosed by it is given by

$A=\oint_{C}xdy =-\oint_{C}ydx=\frac{1}{2}\oint_{C}xdy-ydx$

I think you forgot the minus sign in $-\oint_{C}ydx$

P.S. The value I get is $40\sqrt{6}$