We began Chapter 7 this week in class by first focused on the application of integrals for section 7.1, then switching to finding areas on a plane for section 7.2. For me personally, section 7.1 was the more challenging of the two sections. I think this is because of the fact that the word problems in this section always confused me on what exactly they were asking and how to apply them to the integrals. I kept misunderstanding net area and how it is actually the displacement, whereas total area is the actual distance. It's kind of cool though that we can apply these problems to real life scenarios with positions and speed and distance traveled by objects. Yay math
:-) With section 7.2, I believe I had a better understanding on the material than 7.1. Essentially we're finding the area between two curves on a plane, and the intersection points of the curves are the upper and lower bounds on the definite integral. Once we have the intersection points, we subtract the bottom curve from the top curve (under the definite integral) and solve. Often times we also integrate with respect to y, not x, which at first had me confused, but integrating this way is just as simple as integrating with respect to x. We just keep learning new ways to find new areas under curves. Who knows what shape we'll find next. Check back next week for more details on area!
:-) With section 7.2, I believe I had a better understanding on the material than 7.1. Essentially we're finding the area between two curves on a plane, and the intersection points of the curves are the upper and lower bounds on the definite integral. Once we have the intersection points, we subtract the bottom curve from the top curve (under the definite integral) and solve. Often times we also integrate with respect to y, not x, which at first had me confused, but integrating this way is just as simple as integrating with respect to x. We just keep learning new ways to find new areas under curves. Who knows what shape we'll find next. Check back next week for more details on area!