Tri 2 week 9

This week we started working on chapter six. So far chapter six seems fairly easy to me. A lot if the stuff is almost review. We started with 6.2 which was basically just u substitution again. This came pretty easy to me. There was one tricky part though. We you are finding a definite integral and use u substitution you have to change the bounds. You simply do this be plugging in the original values into what you have for your u equation. The reason you have to do this is because the original bounds are for x but when you use u substitution you are changing the function inside the integral so therefore your bounds must be different. This is a step that I forget every once in awhile so it is an important step to memorize. After 6.2 we worked back to 6.1. In 6.1 we learned about slope fields. With a slope field you graph the slope at every point of a derivative function. The resulting image looks similar to what the antiderivative would look like. These slope fields are helpful for problems that we can't easily antiderive. Some slope fields had patterns that you could pick up on. Others had both an x and a y. That leads into 6.4. In 6.4 we had to antiderive when there was an x and a y in the function. This wasn't as challenging as I origanlly thought it was going to be. Basically all you have to do is get all the y's to one side and then multiply both sides by dx so you can then antiderive both sides. When you antiderive both sides you still aren't done yet. Don't forget that you have to add a plus c to the x side. Most of the problems we had also gave a point. For those you have have to plug the coordinates back in and solve for c. I believe that is all we learned this week.