Integrating (xsinx)^2: Tips and Tricks

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    Integration
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Discussion Overview

The discussion revolves around the integration of the function (xsinx)^2, exploring various techniques and strategies for solving the integral. Participants share their experiences and methods, including integration by parts and trigonometric identities.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • Joe expresses difficulty in integrating (xsinx)^2 using integration by parts and trigonometric identities.
  • One participant suggests that the issue may stem from incorrectly choosing "u" and "v" in integration by parts and recommends using the double-angle formula.
  • Another participant provides the identity sin^2x = (1 - cos2x)/2 as a potential simplification.
  • A participant requests further guidance after attempting the suggested identity without success.
  • Another participant offers a detailed step-by-step approach using integration by parts, suggesting specific choices for "u" and "dv" and encouraging Joe to show his work for better assistance.
  • Joe later confirms that he successfully solved the integral after receiving help.

Areas of Agreement / Disagreement

Participants generally agree on the use of integration by parts and the trigonometric identity, but there is no consensus on the effectiveness of the approaches, as some participants express continued difficulty.

Contextual Notes

Some participants mention that the integration process may involve multiple steps and substitutions, highlighting the complexity of the problem without resolving the specific challenges faced.

Who May Find This Useful

Students or individuals seeking assistance with integration techniques, particularly those involving products of functions and trigonometric identities.

josephcollins
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Hi ppl, I need a little pointer with the integral of (xsinx)^2. I tried by parts but it just doesn't stop and I've tried writing sin^2x in it's other forms but that yields similar results. Any help please?

Joe
 
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If it doesn't stop, it is because you switch what's "u" and "v".
It is definitely smart to use the double-angle formula!
 
Use

[tex]sin^{2}x = \frac{1-cos2x}{2}[/tex]
 
I used the identity suggested, but I don't get anywhere, could u please just take the problem a little further?
 
Show in some detail why you don't get anywhere!
 
By the way, may I "join"? In the first place, do you already know the answer in the first hand? (I mean, you got the answer somewhere else? =) )

Since the members here are not giving you a direct answer to the question... I'll give you some hints... I only did some integration by parts...

1.) let u = sin^2 x and dv = x^2dx... so, du = sin2x dx and v = x^3/3...
2.) You get the 2nd integral, right? If you've done the first step (of mine) correctly, then your on the track..
let u = x^3 and dv = sin[2x] dx... so, du = 3x^2 dx and v = -cos[2x] / 2.
3.) keep doing integration by parts a little more... later, you'll notice something - integration by simple substitution... and then if there's anything to simplify, do so.

Show your work... so that others can guide you...

Cyclovenom's hint for you, unfortunately, does not apply in my strategy that I've written for you here... but still, both different approach, if correctly done, can lead you to the same answer. =) Good luck!
 
Joe, I hope that helps... I'll be watching here.. time to time. =)
 
Thanks for the help irony, I managed it now, cheers,
Joe
 
Welcome... :D
 

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