MAT137Y1 Lecture Notes - Lecture 22: Riemann Sum
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Let"s use four rectangles of equal width of 1. 1. This partitions the interval [0,4][0,4] into four subintervals, [0,1],[0,1], [1,2],[1,2], [2,3] On each subinterval we will draw a rectangle. There are three common ways to determine the height of these rectangles: the left hand rule, the right hand rule, and the midpoint rule: The left hand rule says to evaluate the function at the left-hand endpoint of the subinterval and make the rectangle that height. The rectangle labelled lhr is drawn on the interval [2,3][2,3] with a height determined by the left hand rule, namely f(2)=4. f(2)=4. The right hand rule says the opposite: on each subinterval, evaluate the function at the right endpoint and make the rectangle that height. Rhr is drawn on the interval [0,1][0,1] with a height determined by the right hand rule, namely f(1)=3. f(1)=3. The midpoint rule says that on each subinterval, evaluate the function at the midpoint and make the rectangle that height.
