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numerical integration to approximation of the definite integral

Use numerical integration to approximation of the definite integral using the listed below meth- ods.
1. Methods:
(a) Left Rectangular Rule also known as Lower sum. (b) Right Rectangular Rule also know as upper sum.
(c) Midpoint Rule (d) Trapezoid Rule
(e) Simpson Rule (No Help from anyone for 1% of your Final grade) 2. Evaluate
1
(a) (b) (c)
4
x2 +1dx 32
xsin (x)dx 1
0
0 2
2×3 −2x−5dx
3. Answer the following questions:
(a) Plot each of the function on the given domain (You may use wolfram alpha to plot)
(b) Evaluate the integral using number of rectangle/ trapezoidN = 2, 10, 100, 1000, 10000.
(c) Use command format long to display 16 decimals places.
(d) Keep all result in a table ( Column is the integration methods and Row is number of
rectangles N)
(e) Explain your discovery and show any trend of solution with respect to N. How many
correct digits do you think you get it right?
RUBRIC:
+ Hard copy of the report is due on Monday September 28( MW Class) and Tuesday September 29( TR Class) at the beginning of class.
+Answers all questions and label it.
+ Must type and print all work (explanations, plots and tables) follow by all code attached at the back of the report.
+ You may work with one partner
+ You turn in as many draft as possible to receive 100%.
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