Peicewise Integral Evaluation: Problems and Solutions

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Homework Help Overview

The discussion revolves around the evaluation of a piecewise integral, with participants exploring the correct approach to splitting the integral and addressing potential errors in their calculations.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss splitting the integral into two parts and question the correctness of their evaluations. There is a focus on the implications of using decimal versus fractional representations in calculations.

Discussion Status

The conversation includes attempts to clarify the evaluation process and address errors. Some participants provide guidance on using fractions to avoid rounding issues, while others share their experiences with the computer program used for submission.

Contextual Notes

Participants mention the challenges posed by the computer program's sensitivity to input formats, which may affect the evaluation of the integral.

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Homework Statement


Evaluate the integral
%282%20text%28%20if%20%29%20-2%3C%3Dx%3C0%2C%205-x%5E2%20text%28%20if%20%29%200%3C%3Dx%3C%3D4%29.gif



The Attempt at a Solution


I tried splitting it into two integrals and adding the results, but it says that's wrong. I think it has something to do with the fact that the first part doesn't go all the way to zero...
 
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Splitting up the integral is the correct approach. Show your work so people can see where you go wrong.
 
Ok, so I started by evaluating the first function on the interval [-2,0]

F(x)=2x
F(0)=0
F(-2)=-4

0-(-4)=4

Then I evaluated the second function on [0,4]

F(x)= 5x-x3/3
F(0)=0
F(4)=-1.3333333

Adding them gets me 2.6666666, which apparently is incorrect.
 
Why do you say it is apparently incorrect. Does the book provide an answer or do you enter it in some kind of computer program? Either way your answer is essentially correct, but since you've chosen to use decimals you get rounding errors. Use fractions instead.
 
It is a computer program. I'll try with factions, it is very finicky sometimes...
 
Entered 8/3 and was right. Hate computers! haha
 

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