More Calculus

 Hello, and welcome to my last action project for my workshop, "Introduction to Calculus". In this class, we learned the basics of calculus by reviewing slope formulas from Algebra. Calculus is a branch of mathematics that deals with operations on functions and their derivatives. We recently learned and practiced derivatives and antiderivatives. Derivatives or prime is another function that can be used to find the slope at any point. For this action project, we were instructed to use a nonlinear function incorporating our two random numbers, evaluate our functions, find the derivative and antiderivative (integral), and use the antiderivative to estimate the area underneath a section of the nonlinear function. I hope you enjoy my calculus equations down below!

I chose -6x + x^{6} (x to the 6th power) as my nonlinear function to incorporate the random numbers I was assigned.  

 Here is my process of finding the indefinite integral (aka “antiderivative”) of the function. Here you can see how I differentiated my integral to double-check my work and see if I got my initial function. Finally, I calculated and visualized the area underneath your function using the definite integral.

 

Lastly, I estimated the area underneath a section of it using a Left Riemann sum with function notation. Overall, this process was pretty complex but got simpler step by step. I enjoyed this action project and this calculus workshop. Thanks for visiting my blog and have a great day!