Students! Pi day was a blast and I hope you celebrated by eating some pie ;-) Too bad not everybody in the world celebrated Pi day :-( Check out this short article if you are interested in learning a little more about pi :-)
We all know the area of the circle is given by the formula A=pi*r^2. Thus, the area of the unit circle is pi. Below is a very detailed write up of this fact using Calculus. Since most of you will be taking the course next year, here is a brief description:
In Calculus, finding the integral of a function with respect to x means to find the area from the curve to the x-axis on a specified interval. Also, the integral is usually called the anti-derivative since integrating is the reverse process of differentiation (the concept of finding the slope at any point on a curve or rate of change). So the integral is not only the result of trying to figure out the inverse process of differentiation but also the result of looking at the problem of area under a curve. Calculus is truly a beautiful testament of human ingenuity. It's all about the infinitesimal.
We all know the area of the circle is given by the formula A=pi*r^2. Thus, the area of the unit circle is pi. Below is a very detailed write up of this fact using Calculus. Since most of you will be taking the course next year, here is a brief description:
In Calculus, finding the integral of a function with respect to x means to find the area from the curve to the x-axis on a specified interval. Also, the integral is usually called the anti-derivative since integrating is the reverse process of differentiation (the concept of finding the slope at any point on a curve or rate of change). So the integral is not only the result of trying to figure out the inverse process of differentiation but also the result of looking at the problem of area under a curve. Calculus is truly a beautiful testament of human ingenuity. It's all about the infinitesimal.
The above write up was originally posted by Jeremy Williams.