The topic of this week mostly consisted of evaluating integrals. Like most other math subjects, integrals can be evaluated in multiple different ways. There are the easier ways, and of course, the harder ways. I think that the hardest way to evaluate an integral is by using graphs and knowledge of areas. You would think that this would be really easy because you are actually looking at the graph and have a visual aid to kind of help you along. For me personally however, I like to be able to do the sort of algebra side to it.
Now another way to evaluate an integral is by using the NINT program on the calculator. While this may be the easiest way, it is definitely the least rewarding. This is because when you are just typing things in the calculator, you aren't really processing what you are doing and how it relates to solving the problem. This is where other ways to evaluate integrals (like graphing and using areas) become more important, even if they are harder.
My favorite way to evaluate an integral is by taking the anti-derivative of the function. The step -by-step process to this way is as follows:
1. Take the anti-derivative of the function
2. Plug in the "b" number that is on top of the integral sign
3. Plug in the "a" number that is on bottom of the integral sign
4. Subtract the number you got from the "a" value from the number you got from the "b" value.
This way of evaluating the integral shows you that once you find the anti-derivative of the function, you can plug in values from the biggest number to the smallest number and subtract them in order to get the area. I think that this is a really interesting way to think about how the area under a curve relates to the anti-derivative of that function. I think that the section where we graphed derivatives of functions and so forth has allowed me to visualize what I am doing with integrals.
Now another way to evaluate an integral is by using the NINT program on the calculator. While this may be the easiest way, it is definitely the least rewarding. This is because when you are just typing things in the calculator, you aren't really processing what you are doing and how it relates to solving the problem. This is where other ways to evaluate integrals (like graphing and using areas) become more important, even if they are harder.
My favorite way to evaluate an integral is by taking the anti-derivative of the function. The step -by-step process to this way is as follows:
1. Take the anti-derivative of the function
2. Plug in the "b" number that is on top of the integral sign
3. Plug in the "a" number that is on bottom of the integral sign
4. Subtract the number you got from the "a" value from the number you got from the "b" value.
This way of evaluating the integral shows you that once you find the anti-derivative of the function, you can plug in values from the biggest number to the smallest number and subtract them in order to get the area. I think that this is a really interesting way to think about how the area under a curve relates to the anti-derivative of that function. I think that the section where we graphed derivatives of functions and so forth has allowed me to visualize what I am doing with integrals.