I need to integrate a parametric eqn. can someone help out ?

Question

yuki · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

Don't ask amistre, just jump in, integrate

amistre64 · Answer

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

anonymous · Answer

+ C, you knew this was coming

amistre64 · Answer

ack!!!  lol

amistre64 · Answer

nonono... it on an interval lol

yuki · Answer

oh amistre lol

amistre64 · Answer

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

amistre64 · Answer

amistre64 · Answer

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 :)