You ll be working with the function y f x x 1 5 2 and the

Last updated: 8/19/2023

You ll be working with the function y f x x 1 5 2 and the interval you ll always be concerned about is 2 6 Here s a graph 2 1 3 5 3 2 5 2 1 5t It 0 5 0 1 2 4 5 6 You ll need to have the graph above on paper so you ll need to print it or draw it on paper You ll need at least three copies I ll call them your paper graphs The actual area under the curve on the interval 2 6 is about 17 586 Approximating the area under the curve on the interval 2 6 by using a Riemann sum with 4 equal subdivisions and left hand endpoints gives you R 2 f 2 f 0 f 2 f 4 14 976 Draw the rectangles used for this Riemann sum on one of your paper graphs Do you see where the error for this approximation is Approximating the area under the curve on the interval 2 6 by using a Riemann sum with 4 equal subdivisions and right hand endpoints gives you R 2 f 0 f 2 f 4 f 6 21 314 Draw the rectangles used for this Riemann sum on one of your paper graphs Do you see where the error for this approximation is Now you ll try to improve these approximations Remember the interval you re always working with is 2 6 3 Now still taken to be 4 but don t be restricted by having to take equal subdivisions You should use one of your paper graphs to try to draw the 4 best rectangles to approximate the area under the curve Then add up the areas of the rectangles and what do you get Show all your work indig