How to solve ∫2e^-2/tsin(3t)dt using integration by parts?

  • Thread starter xzibition8612
  • Start date
  • Tags
    Integration
In summary: You'll get an expression for du as a function of t and du as a function of u.In summary, the conversation is about solving an integral involving e^(-t/2) and sin(3t). The person asking the question tried using integration by parts but was not able to solve it. Another person suggested setting u=2e^(-t/2) instead of u=2e^(-2/t) and going the other way with integration by parts. This method is commonly used and the person asking the question was surprised they had not seen it before. There may have been a typo in the original working of the problem.
  • #1
xzibition8612
142
0

Homework Statement


see attachment.


Homework Equations





The Attempt at a Solution


ok so the equation is in the attachment. My question is how did ∫2e...etc. in the first line get solved and get the answer in the second line. I tried integration by parts and set 2e^-2/t as the u and sin(3t)dt as dv and then did the uv-∫vdu, but then i get a ecos(3t) form for the ∫vdu and if i kept doing integration by parts i get never ending esin/cos. Anybody can help me or tell me how to solve this much appreciated.
 

Attachments

  • integral.jpg
    integral.jpg
    11.3 KB · Views: 360
Physics news on Phys.org
  • #2
xzibition8612 said:

Homework Statement


see attachment.


Homework Equations





The Attempt at a Solution


ok so the equation is in the attachment. My question is how did ∫2e...etc. in the first line get solved and get the answer in the second line. I tried integration by parts and set 2e^-2/t as the u and sin(3t)dt as dv and then did the uv-∫vdu, but then i get a ecos(3t) form for the ∫vdu and if i kept doing integration by parts i get never ending esin/cos. Anybody can help me or tell me how to solve this much appreciated.

You cannot set u = 2e^(-2/t); instead, set u = 2 e^(-t/2).

In problems like this, the integral I can be found using integration by parts twice: you will get an equation of the form I = f1(t) + f2(t)*I, so you can solve for I. I am surprised you have not seen this before; it is one of the standard 'tricks'.
 
  • #3
well i apologize if my lack of intelligence offended you, but thanks anyway.
 
  • #4
xzibition8612 said:
well i apologize if my lack of intelligence offended you, but thanks anyway.
Ray Vickson said nothing about your intelligence. He only said that he was surprised that you had not seen, before, a particular, but commonly used, method for this kind of problem. That has to do with experience, not intelligence.
 
Last edited by a moderator:
  • #5
attachment.php?attachmentid=54791&d=1358369123.jpg


You may have a typo in your working of the problem.

The stated problem in the attachment has [itex]\displaystyle \ \ e^{-t/2}\ .\ [/itex] I your Original Post, you are letting u=2e-2/t rather than letting u=2e-t/2 .

In either case, du/dt ≠ e .

[itex]\displaystyle \frac{d}{dt} e^{-t/2}=\frac{-1}{2}e^{-t/2}\ .\ [/itex]Considering the sign and the coefficient of the cosine term, I'm convinced that you should go the other way with integration by parts,
Let u=sin(3t) and dv=2e-2/tdt .​
 

1. What is "Integration tough cookie"?

"Integration tough cookie" is a term used to describe the process of combining two or more different systems or components to work together seamlessly.

2. Why is integration important in science?

Integration allows scientists to combine data, methodologies, and technologies from multiple disciplines to gain a more comprehensive understanding of a topic or problem. It also allows for more efficient and effective research processes.

3. What are the challenges of integration in science?

Some challenges of integration in science include differences in terminology, data formats, and methodologies between different fields, as well as the need for interdisciplinary collaboration and communication.

4. How can scientists overcome integration challenges?

To overcome integration challenges, scientists can use standardized data formats and terminology, establish clear communication channels, and foster interdisciplinary collaborations. Additionally, the use of technology, such as data integration platforms, can help streamline the integration process.

5. What are the potential benefits of successful integration in science?

Successful integration in science can lead to a deeper understanding of complex problems, more accurate and reliable results, and the development of innovative solutions. It can also facilitate the sharing of knowledge and resources between different fields, leading to advancements in multiple areas of research.

Similar threads

  • Calculus and Beyond Homework Help
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
807
  • Calculus and Beyond Homework Help
Replies
12
Views
1K
  • Calculus and Beyond Homework Help
Replies
3
Views
956
  • Calculus and Beyond Homework Help
Replies
15
Views
745
  • Calculus and Beyond Homework Help
Replies
7
Views
641
  • Calculus and Beyond Homework Help
Replies
8
Views
1K
  • Calculus and Beyond Homework Help
Replies
12
Views
942
  • Calculus and Beyond Homework Help
Replies
13
Views
2K
  • Calculus and Beyond Homework Help
Replies
32
Views
2K
Back
Top