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Integrals : Riemann Sum with Diagrams

This question has me going around in circles. I can't make the Sigma symbol on the computer, so I used the word "Sigma" instead. For (c), n is above the Sigma symbol and i=1 is below it.

(a)Find an approximation to the integral as 0 goes to 4 of (x^2-3x)dx using a Riemann sum with right endpoints and n=8.
(b)Draw a diagram to illustrate the approximation in part (a).
(c)Use this equation (the integral as a goes to b of f(x)dx=the limit as n goes to infinity of Sigma f(xi) delta x) to evaulate the integral as 0 goes to 4 of ((x^2)-3x)dx.
(d)Interpret the integral in part (c) as a difference of areas and illustrate it.

Solution Preview

Ok First draw this function from x = 0 to x = 4 I get f(x) values 0,-2,-2,0, and 4.

now divide the x axis into 8 equal sections for 0 to 4 The area of interest is between. The x axis and the curve. The area under the x axis is a negative area and the area above the x- axis ...

Solution Summary

Riemann sums are explained. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

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