How to integrate this? quick question

  • Thread starter NutriGrainKiller
  • Start date
  • Tags
    Integrate
In summary, the person is struggling to remember how to use the trig identity to compute the Fourier series of a function, and is looking for help in solving a specific problem involving two trigonometric functions. They mention a preferred method of not using the identity, but it is unclear why they do not want to use it.
  • #1
NutriGrainKiller
62
0
[tex] \int_{0}^{2 \lambda} \cos({\frac{kx}{2}}) \cos({nx}) dx[/tex]

I can't find my calc2 notes and it's killing me! This thing came up half way through the computation of the Fourier series of [tex]f(x) = A\cos({\frac{\pi x}{\lambda}})[/tex]..and i can't remember how to do it!

I am very aware of the trig identity below, but i would prefer not to use it for obvious reasons.

[tex]\cos{\alpha}\cos{\beta} = \frac{1}{2}[\cos{\frac{(\alpha + \beta)}{2} + \cos{\frac{(\alpha - \beta)}{2}][/tex]

I have the exact same question except instead of two cosines there's one cosine and one sine..any help is appreciated!
 
Last edited:
Physics news on Phys.org
  • #2
What are the obvious reasons? I would think that using that identity would be the "obvious" way to do it!

(Your identity is wrong: there is no 1/2 inside the functions. It is
[tex]\cos{\alpha}\cos{\beta} = \frac{1}{2}[\cos(\alpha + \beta) + \cos{(\alpha - \beta)][/tex])

And
[tex]sin(\alpha)cos(\beta)= \frac{1}{2}[sin(\alpha+ \beta)+ sin(\alpha-\beta)][/tex]
 

1. What is integration in science?

Integration in science refers to the process of combining different pieces of information or data to form a more complete and comprehensive understanding of a particular topic or phenomenon.

2. Why is integration important in scientific research?

Integration is important in scientific research because it allows scientists to make connections and draw conclusions from multiple sources of evidence. This helps to ensure that the findings and conclusions are well-supported and not based on limited or biased information.

3. How do you integrate different scientific disciplines?

To integrate different scientific disciplines, scientists must first identify the areas of overlap and common ground between the disciplines. They can then use this information to develop a framework for integrating the various perspectives and data. This can involve collaboration, communication, and the use of specialized tools and techniques.

4. What are some challenges of integrating different sources of data?

Some challenges of integrating different sources of data include differences in terminology, methods, and quality of data. It can also be difficult to reconcile conflicting or contradictory findings from different sources. Additionally, integrating large amounts of data can be time-consuming and require specialized skills and resources.

5. How can scientists ensure the validity of integrated data?

To ensure the validity of integrated data, scientists must carefully evaluate the sources and methods used to collect and analyze the data. This can involve checking for biases, conducting statistical analyses, and seeking input from other experts in the field. Transparency and reproducibility are also important factors in ensuring the validity of integrated data.

Similar threads

  • Calculus and Beyond Homework Help
Replies
3
Views
487
  • Calculus and Beyond Homework Help
Replies
3
Views
268
  • Calculus and Beyond Homework Help
Replies
3
Views
265
  • Calculus and Beyond Homework Help
Replies
13
Views
1K
Replies
9
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
640
  • Calculus and Beyond Homework Help
Replies
4
Views
869
  • Calculus and Beyond Homework Help
Replies
11
Views
1K
  • Calculus and Beyond Homework Help
Replies
9
Views
698
Replies
12
Views
267
Back
Top