anonymous 5 years ago I need to integrate a parametric eqn. can someone help out ?

1. anonymous

$x_t = 3+\sin(t)$ $y_t = 3- 4\cos(t)$ t from 0 to 2 pi

2. amistre64

its an ellipse starting at the point 3,3 right?

3. amistre64

parametrics are derived seperatley; can you just integrate then seperately as well?

4. anonymous

Don't ask amistre, just jump in, integrate

5. amistre64

x = 3t - cos(t) y = 3t - 4sint(t) then lol

6. anonymous

+ C, you knew this was coming

7. amistre64

ack!!! lol

8. amistre64

nonono... it on an interval lol

9. anonymous

oh amistre lol

10. amistre64

the other option would be to make a rectanuglar coord equation and integrate

11. amistre64
12. amistre64

x = 3t - cos(t); at 0 and 2pi 6pi - 1 - (-1) y = 3t - 4sint(t) ; 0 , 2pi 6pi - 4(0) - 0 6pi -1+1 + 6pi = 12pi... it matches :)

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