After that Mr. K gave us three integrals to antidifferentiate. When solving these three questions you must consider these two derivative rules:
After that Mr. K talked about "Trapezoid Sums" and "Midpoint Sums". I'll sum it all up in four simple diagrams.
For Trapezoid Sums when the curve is concave down, the sum would be an under estimate. When the curve is concave up, the sum would be an over estimate.
For Midpoint Sums, if you rotate it and make it a line tangent to the curve you'll see that when the curve is concave down, the sum would be an over estimate. When the curve is concave up, the sum would be an under estimate.
Well that's all I was able to muster up for this class, as you all know Charlene was the next scribe, her post is already up. Enjoy!
I also have a very important announcement to make. Even though I was convinced to stay in the course by Mr. K himself I truly believe now that it's best if I don't continue on. I experienced something in our last class that couldn't be a better reason for my leaving. I was having trouble with completing a chart, not only because I was unaware of the fact I was doing my task improperly, but also because there was something in there that I SHOULD'VE KNOWN from past pre-calculus courses that I completely forgotten. That explains to me that I haven't done my past math courses to the best of my ability, therefore hindering my learning experiences in my present math courses. I've already begun trying to fix up my past by taking my PRECAL 40S course again. This decision hopefully will allow me to take Calculus again in University, and this time understand things completely with the mind set of thinking I know material I should know and that'll make things easy for me. One last thing, I know Mr. K you tried to keep me in your class and you succeed. However, this time I've decided and no matter how disappointed you may be, I feel this is the right thing for me to do in my life and my soon to be career in education. Please I'm not asking you to agree with me on my decision, but I'd like to know you're always there for me when I need you. I'm terribly sorry Mr. K, but I'm not going to ask for your forgiveness on my decision.