<p>My teacher completely skipped over finding area between parametric and polar curves, and now while I'm working on problems from the Barrons book, they throw questions like these at me all the time.</p>
<p>So can someone give me a tutorial on how to do this, in somewhat detail...I;m a fast learner, so it shouldn't take long...</p>
<p>THANKS A LOT GUYS!!!!!!</p>
<p>try your textbook</p>
<p>vader if you have an AIM I will try to explain it as simply as possible without going through the derivations</p>
<p>For parametric curves, I basically just convert it into cartesian.</p>
<p>For example:
x=sin(t)
y=cos(t)^2</p>
<p>Find the area under the curve from (insert two numbers here).</p>
<p>For this problem, I would just solve for t (t=sin(x)^(-1)), and plug it into the other equation (y=cos (sin(x)^(-1))^2). For the example, this simplifies to y=1-(x^2). Now just find the area like normal.</p>
<p>Polar is more complicated... Check google.</p>
<p>Maybe this will help:</p>
<p>Say you have some function f(x). f(x) is a normal y= some function of x.
It passes the vertical line test.</p>
<p>In order to express f(x) in turns of parametric functions you have</p>
<p>y(t)=f(t)
x(t)=t</p>
<p>notice that substitution gives you back y = f(x)</p>
<p>when you integrate f(x) you have (s= integral symbol)</p>
<p>s f(x) dx = F(x)</p>
<p>to integrate the function parametrically, you can do substitution</p>
<p>x'(t) = dt
y(t)=f(t)</p>
<p>so you have</p>
<p>s y(t) x'(t) (which is how you find the area under a parametric curve with respect to the x axis)</p>
<p>I hope that made it clearer, if not, try HippoCampus.org</p>