1. The problem statement, all variables and given/known data Use GT to find the area of one petal of the 8-leafed rose given by [tex]r=17sin(\theta)[/tex] Recall that the area of a region D enclosed by a curve C can be found by [tex]A=1/2\int(xdy - ydx)[/tex] I calculated it using the parametrization [tex]x=rcos(\theta), y=rcos(\theta)[/tex] And I found a really long integral, evaluated it from 0 to pi/4, and got the correct answer. Here is my question: apparently, if x is defined as above, and I find [tex] dx = -rsin(\theta), dy = rcos(\theta)[/tex], then the integral [tex]A=1/2\int(xdy - ydx)[/tex] simplifies nicely to [tex]1/2\int(r^2)d\theta[/tex]. Evaluating this integral again from 0 to pi/4 gives the correct answer. So... why is it that I can pretend "r" is a constant when I'm evalutating dx and dy, when really, r is dependent on theta just as the x and y parametrizations are?