Today, we’ve done examples, both hard and easy, tricky and straightforward ones today. Here are the notes: wk2day5. There is an added example on evaluating a definite integral using substitution rule (p.13-14). The important thing is about the notation on the integration limits.
There are no new concepts introduced except the symmetry (p.6), and how it plays a role when integrating a symmetric function on a symmetric domain. We focused on problem-solving techniques.
We also covered a few brief word problems, but skipped the really interesting one. The problems with full solutions is here: wordprob2_lecture5_withsol.
Next lecture we’ll jump into the concepts of area between two curves and volume of revolution, the natural next step in calculating the area and volume of any general object! You will need the concept of Riemann sum again! The key will be to slice things up into “thin strips”.
Just like how Riemann sliced our “signed area” picture of a definite integral into many rectangle-like thin strips. The only essential difference is that, this time, the “thin strips” looks just slightly different for the more general area problem, and gets a new dimension for the volume problem.