Definite Integration: 9_0 c/x^3 dx = (3/8)c

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Homework Help Overview

The discussion revolves around the definite integral of the function c/x^3 from 0 to 9, with participants initially suggesting different interpretations of the problem statement and bounds. The subject area is calculus, specifically focusing on integration techniques and evaluation of definite integrals.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the setup of the integral, questioning the bounds and the expression used. There is an exploration of the evaluation process and whether the placement of x^3 affects the outcome. Some participants express uncertainty about their calculations and seek clarification on the correct interpretation of the integral.

Discussion Status

The discussion is active, with participants clarifying the bounds of the integral and confirming their interpretations. Some guidance is provided regarding the expression of the integrand, but there is no explicit consensus on the correct evaluation method or outcome.

Contextual Notes

There is a noted confusion regarding the bounds of the integral, initially stated as 9_0 but later corrected to 2_1. This change appears to influence the evaluation results discussed by participants.

cd246
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Homework Statement


integration 9_0 c/x^3 dx. the answer is (3/8)c.

Homework Equations


just distrib. then plug in the #'s

The Attempt at a Solution


=cx^-3
= (cx^-2)/-2=c/-2x^2
I know it has something to do with distribution.
 
Last edited:
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I assume your problem statement is supposed to represent this(please confirm):

[tex]\int^9_0 \frac{c}{x^3}dx[/tex]

If this is the case, I agree with your answer. When I evaluate the integral at the bounds I do not get the answer you stated. I get -c/162 as an answer. Are you sure that is correct?
 
Last edited:
My apologies, it is 2_1 not 9_0
 
cd246 said:
My apologies, it is 2_1 not 9_0

Ahh if that is the case, then I do get (3/8)c as the answer. Were the bounds your problem, or is there something else?
 
that was pretty much it. did u put x^3 on top? or did you left the x^3 on the bottom? Because i believe that was my problem on this one.
 
cd246 said:
that was pretty much it. did u put x^3 on top? or did you left the x^3 on the bottom? Because i believe that was my problem on this one.

I think it is good practice to write any fraction of c/x^n as cx^-n. I think it makes many problems look less complicated. So, yes, if this is what you mean, I did "put the x^3 on top."
 
ok i got it now. thanx
 
Your Welcome!
 

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