This week we started Chapter 5, and began learning about Definite Integrals. All I know is that I am so glad to be done with Chapter 4 and optimization. I find definite integrals way more interesting and so far have really liked working with them. We use definite integrals to find the area under a curved function. When we graph functions that give us straight lines, we are able to find the area of that shape by using simple area formulas like a=½ bh, but when we graph functions like y=x^2, it’s impossible to find the exact area under the function with basic formulas. Instead of trying to find the area of one shape, we try to add up an infinite number of rectangles that can be drawn under the curve between the given bounds. Definite Integrals allow us to do that. Throughout the week we learned different rules for integrals that showed us how to add/subtract them, multiply them and more. We also learned how to evaluate definite integrals using the antiderivative. When you take the antiderivative of the function, you can plug in the bounds for x, and then solve to get the area. Overall, I feel pretty good about my understanding of this topic so far. Here is a Khan Academy that shows what I tried to explain earlier.
https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/definite_integrals/v/evaluating-simple-definite-integral
https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/definite_integrals/v/evaluating-simple-definite-integral