Integration by Parts: Solve x^2exp(-3x)dx

Click For Summary

Discussion Overview

The discussion revolves around solving the integral of the function x^2 * e^(-3x) using integration by parts. Participants explore various methods and approaches to tackle the problem, including the tabular method and the assignment of variables in the integration by parts formula.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses difficulty in applying integration by parts to the integral of x^2 * e^(-3x).
  • Another participant suggests taking dv = e^(-3x) dx and u = x^2 as a starting point.
  • A question arises regarding the integral of e^(-3x), with a proposed answer of -1/3 * e^(-3x).
  • Confirmation is provided that the integral of e^(-3x) is indeed -1/3 * e^(-3x) by differentiation.
  • One participant mentions that the tabular method could be effective for this integral and asks if others are familiar with it.
  • Another participant indicates uncertainty about the tabular method.
  • A participant shares their derived answer for the integral but expresses uncertainty about its correctness due to lack of solutions for the exercise.
  • One participant mentions that a software tool, Maple, agrees with their answer.
  • There is a reminder to include an arbitrary constant in the final answer.
  • A link to an external resource on the tabular method is provided for further reference.

Areas of Agreement / Disagreement

Participants generally agree on the steps to take in solving the integral, but there is uncertainty regarding the correctness of the final answer and the application of the tabular method. No consensus is reached on the best approach.

Contextual Notes

Some participants express uncertainty about the tabular method, and there is a lack of definitive solutions for the exercise, which may affect the confidence in the derived answers.

cogs24
Messages
30
Reaction score
0
hi guys
just doing some revision and I am stuck on this question

*integral sign* x^2 . exponential ^ -3x . dx

I know i have to use integration by parts, but i just can't seem to get it out
any ideas?
thanx
 
Physics news on Phys.org
HINT:Take [tex]dv=e^{-3x} \ dx[/tex] and [tex]u=x^2[/tex].

U'll figure out what to do next.

Daniel.
 
but, what is the integral of exponential ^ -3x?
 
is it -1/3 *exponential* ^ -3x?
 
Yes,as you can check by differentiation.

Daniel.
 
The tabular method would work great on this question. Are you familiar with this?
 
ok, once i sub u, du, v and dv into the integral by parts formula, i have to assign, u and dv again to:
-1/3 exponential ^ -3x and 2x

so is dv assigned to the exponential again, like in the first case?
 
no, i am not aware of the tabular method, sorry
 
ok, I've got my answer, unfortunately i don't kow if its right, we don't get solutions for this exercise

-1/3 *exponential* ^ -3x . x^2 - 1/9*exponential*^-3x . 2x - 2/27*exponential*^-3x
 
  • #10
Maple agrees, good job.
 
  • #11
Surely,you must add an arbitrary constant wrt "x" to your solution.

Daniel.
 
  • #12
arbitary constant would be + c
 
  • #13
In case you were interested in this method, http://marauder.millersville.edu/~bikenaga/calculus/parts/partspf.html is a link to the explanation. If one of the two terms will eventually differentiate to zero, this method is much less time consuming.

Jameson
 
Last edited by a moderator:
  • #14
i see, thanks for that link, i will probably apply this method from now on
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
4K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 8 ·
Replies
8
Views
4K
  • · Replies 27 ·
Replies
27
Views
4K
  • · Replies 30 ·
2
Replies
30
Views
3K
  • · Replies 6 ·
Replies
6
Views
4K
  • · Replies 11 ·
Replies
11
Views
3K
Replies
5
Views
5K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 3 ·
Replies
3
Views
4K