This week, we revisited and worked more in depth with anti-differentiation with u-substitution. It took a few problems for u-substitution to come back to me, but I feel much better about it and feel that I can use it with more challenging anti-differential problems. One thing that I struggled with on the 6.2 assignment was determining what u should be and where it would be best to plug it in. I would choose a simple u that I thought might work, but after differentiating to get du, I would be stuck because I would not be able to substitute the derivative into the equation anywhere. What I have been trying to do that has helped me a lot is look at the different parts of the equation and see how they relate to one another. If the derivative of one part is equal to another part of the equation, I know that this part would be good to use for u because I will be able to easily substitute du later. I have also gotten better at adjusting and changing the equation, like changing tan x to sin x/cos x for example, to be able to find the best u.
With all the work we have been doing with both definite and indefinite integrals, I think it is important that I remember the difference between the two. Indefinite integrals are families of functions, and definite integrals are values. Definite integrals have bounds and represent the area under a curve.
Definite Integral Indefinite Integral
With all the work we have been doing with both definite and indefinite integrals, I think it is important that I remember the difference between the two. Indefinite integrals are families of functions, and definite integrals are values. Definite integrals have bounds and represent the area under a curve.
Definite Integral Indefinite Integral
We have also began working with slope fields this week, which I think can be tedious to create, but are interesting to look at and use to get a feel of what the equation looks like, as shown in the picture above. I was a little shaky with slope fields on the first day of the lesson, but after working on the slope fields activity with the people in my group, I feel a lot more confident about them. For some, it helps me a lot to write out the grid and see what the slope will be at each coordinate, but for others I feel good about looking at the graph and being able to match it to its equation. I am looking forward to learning more about slope fields and possibly finding out an easier way to create them.