A periodic function is a mathematical function that repeats its values at regular intervals. This means that the function will have the same values at specific points on its graph, known as periods.
The derivative of a periodic function is a new function that represents the rate of change of the original function at any given point. In other words, it tells us how the value of the function is changing at a specific point.
To find the derivative of a periodic function, you can use the standard rules of differentiation, such as the power rule, product rule, and chain rule. However, since the function repeats itself, the derivative will also repeat itself, resulting in a periodic function.
The integral of a periodic function is the inverse operation of differentiation. It represents the area under the curve of the function and can be used to find the total change or accumulation of the function over a given interval.
To calculate the integral of a periodic function, you can use the fundamental theorem of calculus, which states that the integral of a function can be found by evaluating the antiderivative of that function at the upper and lower bounds of the integral. For a periodic function, this will result in a periodic integral as well.