Problem: Definite integral by subtitution

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Homework Help Overview

The discussion revolves around evaluating a definite integral using substitution, specifically focusing on the transformation of variables and the resulting expressions. The subject area is calculus, particularly integral calculus involving substitution techniques.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the substitution of variables, with one suggesting a specific substitution of u = 1 - r^3. Questions arise regarding the derivation of the differential du and its relationship to the original variable r. There is also an inquiry about the negative sign in the expression -3du.

Discussion Status

The discussion is ongoing, with participants exploring the implications of the substitution and clarifying the steps involved in the transformation. Some guidance has been provided regarding rewriting the integral in terms of u and du, but no consensus has been reached on the specific derivation of certain expressions.

Contextual Notes

Participants express uncertainty about the derivation of the differential and the implications of the substitution, indicating a need for further clarification on these aspects. There is also a mention of a desire to understand the process without simply receiving answers.

don.bandar
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Hi everyone, to day I have a problem in dealing with the following question:

and I hope that you help me

here is may question and my try:
[PLAIN]http://img268.imageshack.us/img268/9291/scan0004ov.jpg

wish you all the best
 
Last edited by a moderator:
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If [tex]u = 1 - r^3[/tex], then

[tex]r = (1-u)^{1/3} = \sqrt[3]{1-u}.[/tex]

Your formula for du is actually correct, so why don't you just complete making the substitution and see if you can do the resulting integral?
 
hi dear,
i know that i can do the subtitution.But i want to know how -3du came?

if you could
 
don.bandar said:
hi dear,
i know that i can do the subtitution.But i want to know how -3du came?

if you could

I'm not sure what the question is. You explicitly computed that

[tex]9r^2 dr = - 3 du.[/tex]

The only thing left to do is finish the computation.
 
Evluating Integrals:

evaluate the indefinite integral by using the given substitution to reduce the integral to standard form.

7. [PLAIN]http://img232.imageshack.us/img232/8840/kmnk.jpg


this is the question

i want to know how did -3du come?!

i'm sorry for asking too many questions
 
Last edited by a moderator:
Try the subst:

[tex] u = 1 - r^{3}[/tex]
 
No need to repeat the statement of the problem. Can you try rewriting

[tex]\frac{9r^2 dr}{\sqrt{1-r^3}}[/tex]

entirely in terms of u and du?
 

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