Last week, we had our first test on Tuesday/Wednesday, and we started talking about the application of definite integral. Remember, you can write up the corrections of your mistake from the test and get up to half of the points back and you can come to me for help, even with writing up of the corrections!
We have talked about the first application of definite integrals: to compute area between curves. Same idea as definite integral, we look at the thin long rectangles that approximate the thin long strips, add up all the approximate areas and take the limit. Since we are looking at areas, our heights of rectangles have to be non-negative, and you want to integrate the absolute values of the differences of the functions. Depending on the curves, choose the appropriate direction to cut up your areas!
Next week, we will spend most of our time writing out Riemann sums. The idea of the process is to find expressions of little pieces of element, add them up and take the limit. After the limiting process, you will obtain a definite integral, and we can solve the definite integral with any of the methods we have learned. Next week is going to be very geometric, so get ready to draw pictures!
I will post your homework over the weekend and it will be due next Thursday.
Alright, that is it for all, have a good weekend!