MAT136H1 Lecture : 5.1 Integration & Anti-derivatives Area Estimate Under a Function Question #1 (Easy)

• School: UTSG
• Department: Mathematics
• Course: MAT136H1
• Professor: all

Document Summary

Question #1 (easy): estimating the area under a function. All questions in this subsection ask for area estimation under the given curve using: left endpoints: , right endpoints: , midpoints: . Then asks which estimate is lower, upper, and best estimate. Do not assume that left endpoints always give the lower estimate and the right endpoints give the upper estimate. Given the pattern of the curve, it can be either/or; so make sure to check. The question specifies the number of rectangles to use, so. This affects the width of each rectangles over the interval [ ], so. Now substitute these input values into the sum, and then calculate: using the left endpoints: , using the right endpoints: , using the midpoints: , the midpoints for each subinterval are: , so for [ ], . ; and so forth: as the estimates show, is the lower estimate, is the upper estimate, and is the best estimate.