How Do You Integrate cos[(pi/9)(x^2)]?

  • Thread starter jmrec100
  • Start date
  • Tags
    Integrate
In summary, the technique used to solve the integral of cos[(pi/9)(x^2)] is substitution. This integral cannot be solved using basic integration rules and has a specific range for x. It can be solved analytically, but the answer may involve special functions. The constant (pi/9) in the integrand represents the frequency of the cosine function and affects its period and shape when graphed.
  • #1
jmrec100
1
0

Homework Statement


Integrate cos[(pi/9)(x^2)


Homework Equations


Is there a trig identity for the cos(x^2) ?


The Attempt at a Solution



U=(pi/9)T^2
dU= [2(pi)/9] (T)dT dT= dU/ {[2(pi)/9 (T)]}

Substitute in get cosU dU/ {[2(pi)/9 (T)]} Now what?
 
Physics news on Phys.org
  • #2
jmrec100 said:

Homework Statement


Integrate cos[(pi/9)(x^2)

Do you mean:

[tex]\int \cos\left(\frac{\pi x^2}{9}\right)dx[/itex]

or something else? Are you given integration limits, or are you only asked for the indefinite integral?
 

FAQ: How Do You Integrate cos[(pi/9)(x^2)]?

1. What is the technique used to solve the integral of cos[(pi/9)(x^2)]?

The technique used to solve this integral is called substitution. By substituting u = (pi/9)(x^2), the integral can be rewritten in terms of u, making it easier to solve.

2. Can the integral of cos[(pi/9)(x^2)] be solved using basic integration rules?

No, the integral of cos[(pi/9)(x^2)] cannot be solved using basic integration rules such as power rule or product rule. It requires the use of the substitution technique.

3. Is there a specific range for x when solving the integral of cos[(pi/9)(x^2)]?

Yes, there is a specific range for x when solving this integral. Since the cosine function has a period of 2pi, the range of x should be chosen such that the argument of cosine, (pi/9)(x^2), is between 0 and 2pi.

4. Can the integral of cos[(pi/9)(x^2)] be solved analytically?

Yes, the integral of cos[(pi/9)(x^2)] can be solved analytically using the substitution technique. However, it may result in a complex answer involving special functions such as the error function.

5. What is the significance of the constant (pi/9) in the integrand of cos[(pi/9)(x^2)]?

The constant (pi/9) in the integrand of cos[(pi/9)(x^2)] represents the frequency of the cosine function. It affects the period and frequency of the function, and thus, the shape of the curve when graphed.

Similar threads

Replies
9
Views
517
Replies
15
Views
1K
Replies
9
Views
1K
Replies
1
Views
786
Replies
2
Views
1K
Replies
1
Views
1K
Replies
1
Views
1K
Back
Top