Understanding Integration by Substitution

Click For Summary
SUMMARY

The discussion focuses on the concept of integration by substitution, specifically addressing the transition from d(sin(2010x)) to dx. Participants clarify that this method avoids the use of the variable 'u' and involves integration by parts. The confusion arises from the omission of certain steps in the integration process, which can lead to misunderstandings. Ultimately, the solution provided by Delzac, which resulted in zero, was verified using an online integration calculator.

PREREQUISITES
  • Understanding of integration techniques, specifically integration by parts.
  • Familiarity with trigonometric functions and their derivatives.
  • Basic knowledge of calculus notation and operations.
  • Experience with online integration tools for verification.
NEXT STEPS
  • Study the method of integration by parts in detail.
  • Learn about the differentiation of trigonometric functions, particularly sin(θ).
  • Explore advanced integration techniques, including successive integration by parts.
  • Practice using online integration calculators for complex functions.
USEFUL FOR

Students studying calculus, educators teaching integration techniques, and anyone seeking to deepen their understanding of integration by substitution and parts.

Delzac
Messages
389
Reaction score
0

Homework Statement


[PLAIN]http://img293.imageshack.us/img293/5026/solutoni.png

Hi all,

Can anyone explain what is going on where? I understand that it is a different way of writing the conventional integration by substitution, instead of using the symbol u. The second line, however, especially confuse me. I don't understand how the working changes between d(sin2010x) and dx.



The Attempt at a Solution


I used integration by parts and worked out the answer to be zero.

Double checked with online integration calculator.

Any help would be greatly appreciated.

Delzac
 
Last edited by a moderator:
Physics news on Phys.org
Hi Delzac! :smile:
Delzac said:
The second line, however, especially confuse me. I don't understand how the working changes between d(sin2010x) and dx.

As you say, it start by avoiding using a "u".

The jump you don't understand is an integration by parts in which the […] bit has been omitted because it's zero. :rolleyes:

(never do that in an exam!)

The whole thing is just a (to my mind) rather long-winded and confusing way of doing two successive integrations by parts. :redface:
 
Oh! now i see. Thanks for the help!

Delzac
 

Similar threads

Integral using substitution x = -u
  • · Replies 12 ·
Replies
12
Views
2K
An Integral simplification I don't understand
  • · Replies 28 ·
Replies
28
Views
3K
Improper integral with substitution
  • · Replies 3 ·
Replies
3
Views
2K
A query in integration using method of substitution
  • · Replies 7 ·
Replies
7
Views
2K
Integral that is reduced to a rational function integral
  • · Replies 2 ·
Replies
2
Views
2K
Integrating [(x^2+3)/(x^8+x^6)] dx by Substitution
  • · Replies 4 ·
Replies
4
Views
2K
Trigonometric Substitution Problem w/ Sin Substitution
  • · Replies 2 ·
Replies
2
Views
2K
Finding the Value of an Integral with U-Substitution
  • · Replies 2 ·
Replies
2
Views
2K
Integration problem using u substitution
  • · Replies 12 ·
Replies
12
Views
2K
Help Understanding A Paper - Brachistochrone With Friction
  • · Replies 2 ·
Replies
2
Views
2K