1. Riemann Integration (8) Using your original Project Part 1 function, f. Pick an interval and find the signed area under the curve. Graph and find the area using methods from calculus. (b) Use builtin integration to check your answer. The function scipy.integrate.quad(f, a,b) will ereate a nice numerical cstimate. (c) Program an algorithm to compute the Riemann sum of your function over the interval. You should he able to change the number of rectangles. You may use the right, left, or center but plesse identify which you are using. Compute the errors in the estimate using several different numbers of rectangles and create a table presenting your findings. 2. Other Numerical Integration (s) Create an algorithm for computing either the trapezoid or simpson's rule. Make sure to be able to change the number of intervals. (b) Compute errors on your function f and compare to your other estimates. 3. Start your report and comnment on the following. (8) Describe your findings in words. (b) Discuss why your estimnate was an over or under tstimate. How did the graph show you this. (c) Given a strictly increasing funetion, which algorithm would you choose? What if it was decreasing? What about undulating? The report will be graded by the following criteria: Clean Code- 10 points. Functions and variables are defined with deseriptive names. interpreted with minimal effort. Code can be Report Style 10 points. Your report contains a title, author names, elass it is for, and instructor's name. Functions and Algorithms- 10 points. Functions and algorithms are used where appropriate eimplifying the coding and allowing for case of read and re-usability. Graphing and Tables 10 points. Graphs are presented with appropriate windows and comments are made to help interpret the picture. Tables are included with errors and methods used. Writing Quality 10 point. The paper is readable, clearly written and contains a single voice. There are few, if any, grammatical or spelling errors and they do not interfere with the clarity of the paper. If vo have

1. Ria Integration (a) Uning your original Project Part 1 funetion, J. Pick an interval and find the signed are under the curve. Graph and find the area using methods from calculus, (b) Use biriltin integration to check your suwur. The function scipy.integrate quand(S. ab) will create snice numerical estimate (e) Program an algorithm to compute the Riemann sum of your function over the interviul. You should be able to change the number of rectangles. You may mase the right, left, or center but plesso identify which you are using Compute the errors in the estimate using several different members of rectangies and create a table presenting your findings 2. Other Numerical Integration (a) Create an algorithm for computing either the trapezoid or simpeon's rule. Malas sure to be able to change the number of intervis (b) Compute errors on your function and compare to your other estimates 3. Start your report and comment on the following (6) Describe your finding in words (b) Discun why your estimate was in over or under lastimate. How did the graph show you thin. (0) Givens strictly increasing function, which algoritlum would you choos? Whist if it was decreasing? What shout undulating? The report will be graded by the following criteria: Clean Code- 10 points. Function and variables are defined with descriptive times Code can be interpreted with minimal effort. - Report Style - 10 points. Your suport contains a title thor tamen, clous it is for, and iretractors Function and Algorithms - 10 points. Function and algoritha sro ined where appropriate simplifying the coding and allowing for use of rand and ro-rosability mindThis - 10 points. Graphs are pretted with appropriate windows and comme made to help interpret the picture. Thule so included with errors and methods .Writing Quality - 10 point. The paper la readable, clourly written and contains the Theme are few, if any, mal or pelling erron and they do not interfere with the city of the pape ya ay to shout the went foel free to me join in office hours