Efficient Integration of x(e^(-x-theta)): Tips and Solutions

  • Thread starter Thread starter confused88
  • Start date Start date
  • Tags Tags
    Integration
Click For Summary

Homework Help Overview

The discussion revolves around the integration of the function x(e^(-x-theta)), which falls under the subject area of calculus, specifically focusing on integration techniques.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore various substitution methods and integration by parts as potential approaches to solve the integral. There is a mention of checking the original poster's work and the use of attachments for further clarification.

Discussion Status

Some participants have provided alternative methods for approaching the integral, including substitution and factoring techniques. There is an acknowledgment of the original poster's attempt, and guidance has been offered without reaching a consensus on the best approach.

Contextual Notes

The original poster's attachment containing their work is pending approval, which may limit the ability to fully assess their approach. Additionally, there is an emphasis on the use of integration by parts in the discussion.

confused88
Messages
22
Reaction score
0

Homework Statement


Can someone please help me with integration of x(e^(-x-theta)) Thank you. My working is shown below

The Attempt at a Solution


u = x, du = 1 dx, dv = e^(-x-theta)) v = e^-x+theta+1 / theta + 1

the rest can be seen in the attachment. Can you please check it out, it would be greatly appreciated.Thanks
 

Attachments

  • integration.jpg
    integration.jpg
    27 KB · Views: 389
Physics news on Phys.org
The attachment is pending approval so I can't see it.

Use the substitution u = -x - \theta \Rightarrow x = -(u+\theta) \Rightarrow dx = -du. So our integral is now \int (u + theta)e^u du.

Now use integration by parts.
 
ohhh wow thanks a lot!
 
The first thing I would do is write e^{-x- \theta}= e^{-x}e^{-\theta} and factor out the e^{-\theta}. Your integral is just e^{-\theta}\int xe^{-x}dx which can be done by integration by parts.
 

Similar threads

  • · Replies 22 ·
Replies
22
Views
3K
Replies
7
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
14
Views
2K
Replies
6
Views
2K
Replies
4
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 14 ·
Replies
14
Views
2K
Replies
19
Views
3K