Integration and taylor expansion

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Discussion Overview

The discussion revolves around the integration of the function e^(-2x) * x^2 with a focus on different methods to approach the problem, including substitution and integration by parts. Participants express uncertainty and seek assistance in solving the integral.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • Some participants suggest using substitution to solve the integral, but others express that this method has not been successful for them.
  • One participant proposes integration by parts as a viable method to tackle the integral.
  • Another participant provides a specific approach using integration by parts, detailing the choice of u and dv.
  • A later reply indicates that a participant found clarity after receiving guidance, suggesting that they were previously unsure about the integration process.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best method to start the integration, with some advocating for substitution and others for integration by parts. The discussion remains unresolved regarding the most effective approach.

Contextual Notes

Some participants express frustration with their attempts at substitution, indicating that their previous efforts did not yield results. There is a lack of clarity on the specific steps or reasoning behind the proposed methods.

casanova2528
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can anybody help me with this integration?

Integral of e to the -2x times x squared dx

it expands to 1/4, but I'm not sure how to start.
 
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casanova2528 said:
can anybody help me with this integration?

Integral of e to the -2x times x squared dx

it expands to 1/4, but I'm not sure how to start.
Hey casanova, welcome to PF!

You don't really need a Taylor expansion here, how about trying a substitution?
 
I have tried substitution

I've already tried substitution.

argh!

i've tried u = e ^ -2x

I've also tried u = x squared.

it doesn't work!

HELP!
 
Integrate by parts and it works.
 
start me off

with what do I start?
 
casanova2528 said:
with what do I start?

you start by integrating

[tex]\int xe^{-2x}dx[/tex]

by parts.
 
You integrate by parts. Start with x squared. You get

u = x^2
du = 2x dx

dv = e^-2x dx
v = -1/2 e^-2x

Give it a shot from there.
 
thanks

i get it now...just needed a refresher...thanks a lot!
 

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