- The mean value of a function over an interval is the integral of the function divided by the length of the interval.
- The RMS value of a function over an interval is the square root of the integral of the square of the function divided by the length of the interval.
- The trapezoidal rule approximates the area under a curve by dividing the area into trapezoids.
- Simpson's 1/3 rule approximates the area under a curve by dividing the area into parabolic segments
Important Formulas to Remember in these topic
$$\text{Mean value } = \frac{1}{b-a}\int_a^b f(x)dx$$
$$\text{RMS value } = \sqrt{\frac{1}{b-a}\int_a^b [f(x)]^2 dx}$$
$$\text{Trapezoidal rule } = \frac{b-a}{2n}[f(x_0) + 2f(x_1) + 2f(x_2) + \dots + 2f(x_{n-1}) + f(x_n)]$$
$$\text{Simpson's 1/3 Rule } = \frac{b-a}{6}\left[f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + \dots + 2f(x_{n-2}) + 4f(x_{n-1}) + f(x_n)\right]$$