1. The problem is to find the mean (average) value of a function over a given interval. 2. The formula for the mean value $M$ of a continuous function $f(x)$ over the interval $[a,b]$ is: $$M = \frac{1}{b-a} \int_a^b f(x) \, dx$$ This formula calculates the average height of the function on the interval. 3. Important rules: - The function must be integrable on $[a,b]$. - The interval $[a,b]$ must be specified. 4. To find the mean, first compute the definite integral $\int_a^b f(x) \, dx$. 5. Then divide the result by the length of the interval $b-a$. 6. This gives the average value of the function on $[a,b]$. If you provide a specific function and interval, I can calculate the mean value step-by-step.