In another question, the limits change. How do I tell if the function is a closed curve?
The question is "Find the area inside the smaller loop of the limacon r = 1+2cos(\theta)."
The books gives the limits 2(\pi)/3 to 4(\pi)/3."
Find the area of the region in the plane enclosed by the cardioid r = 4+4\sin{\theta}
The book explains that "Because r sweeps out the region as {\theta} goes from 0 to 2{\pi}, these are our limits of integration."
I found an interesting pdf on Tabular IBP.
http://www.maa.org/pubs/Calc_articles/ma035.pdf
Tabular IBP is pretty neat and much faster than classic IBP in some cases. Thanks paulfr.
I took Calculus AB my senior year of high school and I'm also just entering undergraduate. Currently, I'm teaching myself the BC material. I suggest buying Cracking the AP Calculus AB & BC Exams by Princeton Review for $20. It's pretty helpful. Each chapter there are examples that are explained...
The past few examples in my review book demonstrated u-substitution to integrate trig functions. The example I'm on suddenly shows integration by parts. The book doesn't explain why this method is used over u-sub.
\int[SIZE="4"]sec3x dx
In what situation am I supposed to use one method over...