Winter break was relaxing and a great time to stray away from thinking of math. Lo and behold, we're back.
Diving into a new year we also tackled a new topic: The Definite Integral. Essentially we all we are doing is finding area under curves which is called integral calculus.
I was gone when learning about 5.1, but I believe I understand the gist of it. It talked about learning about estimating with finite sums and how it provides the foundation for understanding integral calculus. A way to find areas was to approximate by using rectangles. There are three ways that I know of, LRAM, MRAM, and RRAM; left hand endpoint, midpoint rectangular, and right hand endpoint rectangular approximation method. The different names indicates the different types, for example a midpoint (as seen in picture) would evaluate the function at the midpoint of each sub interval.
Riemann Sums also deal with LRAM, MRAM,and RRAM (all examples of R. Sums). All continuous functions are integral. Meaning, if a function is continuous on an interval [a,b] then its definite integral over [a,b] exists.
This is a new concept to me, and as new concepts in calculus it is only going to take trial and error to really understand and feel comfortable come testing.
Diving into a new year we also tackled a new topic: The Definite Integral. Essentially we all we are doing is finding area under curves which is called integral calculus.
I was gone when learning about 5.1, but I believe I understand the gist of it. It talked about learning about estimating with finite sums and how it provides the foundation for understanding integral calculus. A way to find areas was to approximate by using rectangles. There are three ways that I know of, LRAM, MRAM, and RRAM; left hand endpoint, midpoint rectangular, and right hand endpoint rectangular approximation method. The different names indicates the different types, for example a midpoint (as seen in picture) would evaluate the function at the midpoint of each sub interval.
Riemann Sums also deal with LRAM, MRAM,and RRAM (all examples of R. Sums). All continuous functions are integral. Meaning, if a function is continuous on an interval [a,b] then its definite integral over [a,b] exists.
This is a new concept to me, and as new concepts in calculus it is only going to take trial and error to really understand and feel comfortable come testing.