MATH 115 Chapter Notes - Chapter 6: Mean Value Theorem, Riemann Sum
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Chapter 6 applications of integrals: we use integrals to find areas of regions that lie between the graphs of two functions. approximation to what we intuitively think of as the area of s. The riemann sum: we define the area a of the region s as the limiting value of the sum of the areas of these is an approximating rectangles. If the cross-section is a washer: formula for the volume of a cylindrical shell: 6. 3 volumes by cylindrical shells: and it can be remembered as v = [circumference][height][thickness] In the case of constant acceleration: w = fd work = force x distance. 6. 5 average value of a function: 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.
