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13 Nov 2019
Please explain and answer every part of the question:
Presentation problem 2. (15 points) Consider the definite integral of the function f(x) = 3-x2 on [1,2]. In order to estimate its value, the interval [1,21 is first partitioned into N subintervals of equal length, then a point c is chosen in each subinterval [xz-1,x] and the Riemann sum Sp is formed. (a) (5 points) Write down the expression for Lv, the Riemann sum corresponding to always choosing ck to be the left endpoint of the corresponding subinterval. The value Lv is known as the left endpoint approximation (b) (5 points) Write down the expression for Rn, the Riemann sum corresponding to always choosing ck to be the right endpoint of the corresponding subinterval. The value Rv is known as the right endpoint approximation.
Please explain and answer every part of the question:
Presentation problem 2. (15 points) Consider the definite integral of the function f(x) = 3-x2 on [1,2]. In order to estimate its value, the interval [1,21 is first partitioned into N subintervals of equal length, then a point c is chosen in each subinterval [xz-1,x] and the Riemann sum Sp is formed. (a) (5 points) Write down the expression for Lv, the Riemann sum corresponding to always choosing ck to be the left endpoint of the corresponding subinterval. The value Lv is known as the left endpoint approximation (b) (5 points) Write down the expression for Rn, the Riemann sum corresponding to always choosing ck to be the right endpoint of the corresponding subinterval. The value Rv is known as the right endpoint approximation.
Lelia LubowitzLv2
5 May 2019