http://calc3.askbot.com/questions/Open source question and answer forum written in Python and DjangoenCopyright Askbot, 2010-2011.Wed, 02 Jul 2014 07:44:06 -0500http://calc3.askbot.com/question/45/finding-the-distance-traveled-over-a-length-of-time-of-an-object/Questions 1c and 2 on the review test as us to find an integral that could be solved in order to find the distance traveled by an object over a parametric plot. I can visualize this process, however, I am not quite sure how to go about setting up an integral for this using both \vec{x} = t + cos(4t) and \vec{y} = -sin(4t). Here question 1c is asking us to find the integral described above for the following vector $$ \vec{p}(t) = \langle t + cos(4t), -sin(4t) \rangle $$ and $$ \vec{p'}(t) = \langle 1 - 4sin(4t), -4cos(4t) \rangle $$ I believe setting up the integral would set up using the derivative of the position function integrated over the time interval giving the integral $$ \int_0^{2\pi} \ <1 - 4sin(4t), -4cos(4t)> \mathrm{d}t $$ Any help would be appreciatedKyoukoWed, 02 Jul 2014 07:44:06 -0500http://calc3.askbot.com/question/45/