This week, we began working with definite integrals and anti-derivatives. I really like what we have been learning this week because I am beginning to see the tips and tricks to finding areas quicker and in easier ways. I think its interesting that anti-derivatives can be used to find the area under a curve, and I think this method is much easier than using RAM.
The different ways of evaluating integrals include analyzing the graph of the function and solving for the area using geometry, using the program nINT on a calculator, and solving using the anti-derivative of the function and the given bounds. I think that it is important that we learned all three methods of evaluating areas because they each have their advantages and disadvantages, and together they allow you to see the big picture. The method that may be easiest to understand is the first method in which we look at the graph of the function. Having a visual representation of what you are looking is very helpful, but this method does take much longer than the others and may be hard to use if there are no known area equations to use for a particular shape. Evaluating integrals with the use of anti-derivatives is my favorite method. With this method, the bounds are plugged in to the anti-derivative of the function and subtracted from one another. The reasoning behind this method is a little harder to visualize but makes sense because the anti-derivative shows the net area of a function. When it is evaluated with the bounds, it is equal to the area between those bounds. The nINT program on the calculator is the fastest and easiest way of evaluating definite integrals, but does not provide for an understanding of how the answer was found.
I like how we spent time learning to use each different method because together, they allow me to see the big picture and have a deeper understanding of exactly what we are trying to find and how we are finding it with each method. When I solve a definite integral problem, I like being able to use the anti-derivative to evaluate the integral, and then check my answer by looking at the graph and using the nINT program.
The different ways of evaluating integrals include analyzing the graph of the function and solving for the area using geometry, using the program nINT on a calculator, and solving using the anti-derivative of the function and the given bounds. I think that it is important that we learned all three methods of evaluating areas because they each have their advantages and disadvantages, and together they allow you to see the big picture. The method that may be easiest to understand is the first method in which we look at the graph of the function. Having a visual representation of what you are looking is very helpful, but this method does take much longer than the others and may be hard to use if there are no known area equations to use for a particular shape. Evaluating integrals with the use of anti-derivatives is my favorite method. With this method, the bounds are plugged in to the anti-derivative of the function and subtracted from one another. The reasoning behind this method is a little harder to visualize but makes sense because the anti-derivative shows the net area of a function. When it is evaluated with the bounds, it is equal to the area between those bounds. The nINT program on the calculator is the fastest and easiest way of evaluating definite integrals, but does not provide for an understanding of how the answer was found.
I like how we spent time learning to use each different method because together, they allow me to see the big picture and have a deeper understanding of exactly what we are trying to find and how we are finding it with each method. When I solve a definite integral problem, I like being able to use the anti-derivative to evaluate the integral, and then check my answer by looking at the graph and using the nINT program.