Spring+Week+05

toc =Monday 2/1/10= Today, we went over a homework problem involving an application of the integral. We determined her acceleration at a specific time, and used integrals in order to find specific areas that represent distances. This allowed us to find the total distance Caren traveled. The integral of the absolute value of the function allowed us to find the total distance traveled, while the integral of the function allowed us to determine the distance Caren's home was from her school. == == =Tuesday 2/2/10=

= = =Wednesday 2/3/10= Today we learned how to find the area of shapes formed by the rotation of functions around the x-axis. These slides are the problems we used to learn how: media type="custom" key="8417492" = = =Thursday 2/4/10= Today we learned about the washer method. Whole - hole. The washer method consists of getting the volume of an entire solid and subtracted the unwanted solid out of its volume by finding the volume of the inner unnecessary part.

And we continued to practice this method for the entirety of class. =Friday 2/5/2010= In class, we had the problem of the day reviewing the washer method(as seen in first picture). Then, we learned a new type of volume problem where the problem gives the base of the shape and the type and orientation of the shape above it. These are called Volume with Constant Cross Sections. In order to solve this type of problem, remember that the Volume of the Cross section = (area of the cross section)(thickness). Then once you have this equation, we can convert it to a definite integral and shrink the thickness. Remember to make sure the differential and the equation are using the same variable and if necessary substitute the variable using the original equation of the problem. In order to have a visual of these types of problems, Mrs. Gentry showed us a computer program that generated 3-D images. In all, we have reviewed problems with area and volume, and within the volume problems, we know the washer method, disc method, and now the cross section method.