Research Assignment: Riemann Sums and Area

Research Georg Riemann and write a one-page biography. Make sure that you include at least one fact from his personal life that is not related to mathematics and is not included in your textbook.
Explain the definition of a definite integral using Riemann sums. See the Riemann sum section in your textbook.
Illustrate the use of a Riemann sum to find a definite integral.
Identify each feature of the definition in your example.
Illustrate the definite integral with a graph that shows an example of a Riemann sum.

step-by-step explanation:

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step-by-step explanation:

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when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: