Today, we’ve covered the geometric problem of area bounded by two curves (Section 6.1). The key points
- we want area in the usual sense, not “signed area” which is the default output of a definite integral
- the Riemann sum method works just fine, and the novelty is at the height of each rectangle
- to avoid negative values, which is wrong now, we need to subtract the the lower function value from the upper function value to get the correct height of each rectange
- sketch the picture using the graphs of functions, then interpret the area as a sum of definite integrals
- calculate location of special points (endpoints and points of intersection), these will be basic algebraic problems
- write down and evaluate integrals (techniques learned in Section 5)
Each step in the procedure requires a different kind of skill, but my study tip for you now is that you should really emphasize the first step and practice deliberately by attempting to visualize area problems, do the labeling and write down the correct integrals which mean each part of the area you’re looking for.
The file is here: wk3day6.