What is the true meaning of area in integration?

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Homework Help Overview

The discussion revolves around the interpretation of area in the context of integration, specifically focusing on the integral of the function \(y = x - 2\) over the interval from -2 to 5. Participants are attempting to understand their calculations and the meaning behind the results they are obtaining.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are sharing their calculations and questioning the correctness of their results. There is a focus on understanding what the integral represents in terms of area under the curve, and some are expressing confusion about discrepancies between their answers and expected results.

Discussion Status

The discussion is ongoing, with participants seeking clarification on their calculations and the underlying concepts. Some guidance has been offered regarding the interpretation of area in integration, but there is no explicit consensus on the correct approach or solution yet.

Contextual Notes

There are indications of confusion regarding the use of notation and the interpretation of the integral's result, as well as a mention of an online assignment system providing feedback that suggests an answer of 12.5, which is not aligned with the participants' calculations.

Starrrrr
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1. f_-2^{5} 1x-2dx.2. 1. f_a^{b}f(x)dx3. x^2/2 -2(x)|_-2^5
25/2-2(5)-(4/2-2(-2))=-7/2

What am I doing wrong?
 
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Starrrrr said:
1. f_-2^{5} 1x-2dx.2. 1. f_a^{b}f(x)dx3. x^2/2 -2(x)|_-2^5
25/2-2(5)-(4/2-2(-2))=-7/2

What am I doing wrong?

What makes you think you have done something wrong?
 
Ray Vickson said:
What makes you think you have done something wrong?
When I put the answer to my online assignment thing it says incorrect
 
Ray Vickson said:
What makes you think you have done something wrong?
Allegedly the answer is 12.5 but I don't know how the computer got that
 
Please take some time to look at our LaTeX tutorial - https://www.physicsforums.com/help/latexhelp/. Your post is just about incomprehensible.

Starrrrr said:
1. f_-2^{5} 1x-2dx.2. 1. f_a^{b}f(x)dx3. x^2/2 -2(x)|_-2^5
25/2-2(5)-(4/2-2(-2))=-7/2

What am I doing wrong?
 
Mark44 said:
Please take some time to look at our LaTeX tutorial - https://www.physicsforums.com/help/latexhelp/. Your post is just about incomprehensible.

So you must think more about the meaning of the word "area". Draw the graph of ##y = x-2, \: -2 \leq x \leq 5##. What are you actually computing when you calculate the integral ##\int_{-2}^5 (x-2) \, dx##?
 

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