Solving Int. sin(9x)sin(16x)dx w/o Multiple Angles

In summary, there is another way of solving the integral \int sin(9x)sin(16x)dx using the identity \sin u = \frac{e^{iu}-e^{-iu}}{2i} and expanding the sine in terms of exponential. This method involves multiplying and regrouping the terms into 2 cosine functions. While it may seem more difficult than using the multiple angles formula, it may be easier for some individuals to remember and can be done mentally. The final answer is 1/14 sin7x - 1/50 sin25x.
  • #1
ProBasket
140
0
[tex]\int sin(9x)sin(16x)dx[/tex]

is there another way of solving the problem above besides using the multiple angles formula?
 
Physics news on Phys.org
  • #2
use this identity:

[tex]
sin u = \frac{e^{iu}-e^{-iu}}{2i}
[/tex]

edit:
expand the sine in term of exponential, multiply them and regroup them into 2 cosine, then do the integral
 
Last edited:
  • #3
wow looks more difficult than using multiple angles formula. i just thought there's an easier way to do it so i won't have to remeber crazy amount of formulas when it's test day.
 
  • #4
ProBasket said:
[tex]\int sin(9x)sin(16x)dx[/tex]

is there another way of solving the problem above besides using the multiple angles formula?

use

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

ehild
 
  • #5
actually, my way is much much much more easier than remember you formulas...
I can eye ball the answer using my way...
the answer is...
1/14 sin7x - 1/50 sin25x
the expansion of the complex number is easy... there are only 4 terms
 
The 5 most frequently asked questions about "Solving Int. sin(9x)sin(16x)dx w/o Multiple Angles"

What is the formula for solving the integral sin(9x)sin(16x)dx?

The formula for solving the integral sin(9x)sin(16x)dx is ∫sin(9x)sin(16x)dx = -1/2cos(25x) + 1/4cos(7x) + C.

Why do we need to solve this integral without using multiple angles?

Solving this integral without using multiple angles allows for a simpler and more efficient solution, as using multiple angles can often make the problem more complex and time-consuming.

What are the steps for solving this integral without using multiple angles?

The steps for solving this integral without using multiple angles are as follows: 1) Use the product-to-sum formula to expand the integrand, 2) Simplify the resulting expression using basic trigonometric identities, 3) Integrate each term separately, and 4) Combine the results to get the final solution.

Can I use substitution to solve this integral?

Yes, you can use substitution to solve this integral. However, it may result in a more complex solution and may require using multiple angles.

What are some common mistakes to avoid when solving this integral without using multiple angles?

Some common mistakes to avoid when solving this integral without using multiple angles include: forgetting to use the product-to-sum formula, making errors when simplifying the expression, and forgetting to add the constant of integration.

Similar threads

  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Calculus
Replies
4
Views
2K
  • Calculus and Beyond Homework Help
Replies
11
Views
623
  • Introductory Physics Homework Help
Replies
1
Views
962
  • Calculus and Beyond Homework Help
Replies
7
Views
606
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
27
Views
3K
  • Calculus and Beyond Homework Help
Replies
22
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
2K
Back
Top