Textbook Guide Mathematics: Mean Value Theorem, Riemann Sum

• School: UTSG
• Department: Mathematics
• Course: MAT133Y1
• Professor: all

Document Summary

We use integrals to find areas of regions that lie between the graphs of two functions. The riemann sum is an approximation to what we intuitively think of as the area of s. We define the area a of the region s as the limiting value of the sum of the areas of these approximating rectangles. The volume of a cylinder: v = ah. Formula for the volume of a cylindrical shell: And it can be remembered as v = [circumference][height][thickness] In the case of constant acceleration: w = fd work = force x distance. If f is measured in newtons and d in meters, then the unit for w is a newton-meter, which is called a joule (j). The work done in moving the object from a to b: To calculate the average value of finitely many numbers: We define the average value of f on the interval [a,b] as.