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Estimating the Area under the Curve

Please see the attached file for the fully formatted problems.

1. Graph . Using the formula for the area of a rectangle to find the function: . What is ?
2. Graph . Using the formula for the area of triangles (or trapezoids) to find the function: . (assume that ) What is ?

3. Based on the graph sketched to the left, fill out the table of . What for value of in the interval is minimum? (Hint: you see the graph of not )

4. Find . 5. Find . 6. Find . 7. Find . 8. Find .


Solution Summary

The area under the curve is found using geometric means and integrals. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.