Using MathJax for html math notations should be fun. There are video tutorials.
For WordPress, there are plugins such as wpmathpub.
There is another project program I could make, to leech solutions off chegg, before the trial which I just found out, expires. Though I'd say the solutions are 98% not 100% correct, due to careless contributors.
In Section 6.3, Professor Islam M. asked for proof of circle. Of course, we learned the longest (Calculus) version today. There are two other versions:
2. Sum of infinite sector areas (triangle) ie. 8s (8 triangle-octagon) replaces 2pi(r) in r/2 * (2pi(r)).
3. Area by integrating perimeter of circle from t=0 to t=r in 2pi(t).
In section 7.3 (Text book: Essential Calculus Single Variable 2nd Ed by James Stewart), Volume by Cylindrical shells, I stumbled upon the question where if area is bounded by y=sqrt(x), y=2 and rotates around x-axis. I found the solution, but I was not able to understand why the integration could be int 2pi*x*sqrt(x) dx from 0 to 4, which is not the same as the right method: int 2pi*y*y^2 dy from 0 to 2.
This is due to the fact that dx or dy has to refer to r (radius) which would be x or y respectively. But in the first integration, r = sqrt(x), thus it does not correspond to dx = change of x = change of radius.
For Section 7.6, #17(a), I was baffled at how the integration from a to b was structured as from b to a. My last conclusion was that it has to do with how integration works with positive & negative results.
Formulas to remember
Logarithm
rate of change
Trigonometry