Math Help - Complicated Curve Length

1. Complicated Curve Length

Compute the length of the parametric curve
x=(t2−2)sint+2tcost
y=(2−t2)cost+2tsint

from t1=0 to t2=

I know that I need to square the derivatives, and then add them together, and square root them, and then integrate. Is there anyway to uncomplicate the terms before I start doing the derivative? As it stands, it looks like it will be unnecessarily complicated...

2. Originally Posted by Hellreaver
Compute the length of the parametric curve
x=(t2−2)sint+2tcost
y=(2−t2)cost+2tsint

from t1=0 to t2=

I know that I need to square the derivatives, and then add them together, and square root them, and then integrate. Is there anyway to uncomplicate the terms before I start doing the derivative? As it stands, it looks like it will be unnecessarily complicated...
If you take the two derivatives, square them and add (and simplify) you should end up with

$x_t^2 + y_t^2 = t^4$

3. AH! Sorry, I copied the question down wrong...

Compute the length of the parametric curve
x=(t^2−2)sint+2t cost
y=(2−t^2)cost+2t sint

I don't know if that changes anything. Sorry again, I was in a hurry as I needed to get a 2000 word english essay done...

4. Originally Posted by Hellreaver
Compute the length of the parametric curve
x=(t2−2)sint+2tcost
y=(2−t2)cost+2tsint
With your original post, the placing of the two in t2 suggested that it was t^2 and that's what I assumed (I know assuming is bad). So my answer is still good.

5. Ok awesome. Thanks so much. I just had to check, because it was a dumb mistake on my part.