Estimating area under the graph

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SUMMARY

The discussion focuses on estimating the area under the graph of the function f(x) = 3 + x² from x = -1 to x = 2 using six approximating rectangles and right endpoints. The user initially attempts to calculate the area using a summation formula but incorrectly applies the right endpoint method. The correct approach involves determining the heights of the rectangles at the right endpoints: -0.5, 0, 0.5, 1, 1.5, and 2, rather than starting from -1. Visual representation of the rectangles is also recommended for better understanding.

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  • Understanding of Riemann sums
  • Familiarity with the function f(x) = 3 + x²
  • Knowledge of right endpoint approximation methods
  • Basic graphing skills to visualize functions and rectangles
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  • Study the concept of right endpoint approximations in calculus
  • Practice drawing graphs and estimating areas under curves
  • Explore the use of numerical integration techniques
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Students studying calculus, particularly those learning about integration and area estimation techniques, as well as educators looking for examples of Riemann sums and graphical representations.

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Homework Statement



Estimate the area under the graph of f(x)=3+x^2 from x=−1 to x=2 using six approximating rectangles and right endpoints.






The Attempt at a Solution



I've tried this multiple times but can't seem to get it, can someone tell me if i am on the right track?

i have

summation [3/6(3+(-1+i/6)^2)]

where i starts at -1 and increases by .5 passing through (-1,-0.5,0,0.5,1,1.5)

(I'm not sure about how the i increases)

Can anyone tell me what i am doing wrong?
 
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Start with a picture of the problem.

Show the widths and heights of your 6 rectangles.
 
hahaha158 said:

Homework Statement



Estimate the area under the graph of f(x)=3+x^2 from x=−1 to x=2 using six approximating rectangles and right endpoints.






The Attempt at a Solution



I've tried this multiple times but can't seem to get it, can someone tell me if i am on the right track?

i have

summation [3/6(3+(-1+i/6)^2)]

where i starts at -1 and increases by .5 passing through (-1,-0.5,0,0.5,1,1.5)
This is an error. Because you are using right endpoints, the heights of the rectangles are determined at -0.5, 0, 0.5, 1, 1.5, and 2.

(I'm not sure about how the i increases)

Can anyone tell me what i am doing wrong?
I would second SteamKing's suggestion that you actually draw the rectangles. You seem to be trying to apply a formula without understanding it.
 

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