Final answer:
The student is asking how to calculate a Riemann sum for a function within an interval [a,b]. It involves dividing the interval into subintervals and summing the areas of rectangles determined by the function's value at certain points multiplied by the subintervals' width.
Step-by-step explanation:
The student's question pertains to calculating the Riemann sum for a function over a specific interval [a,b]. The Riemann sum is an approach to approximate the integral of a function over an interval by dividing the interval into smaller subintervals, and then summing up the areas of rectangles whose heights are determined by the function values at specified points within the subintervals. To calculate the Riemann sum, the limits of integration (a and b) first need to be established.
We are also considering various equations for the calculation of properties such as area under a curve and probability density functions. The question references the use of limits and integrals, involving differential elements (dm, dìhi, etc.) which are typical for physical and mathematical problems involving continuous distributions.
To provide the student with a formula for the Riemann sum, one would typically choose either left, right, or midpoint evaluation points for the function within each subinterval, then multiply each function value by the width of the subinterval and sum the results. The more subintervals used, the closer the Riemann sum will approximate the actual integral, especially as the number of subintervals approaches infinity.