# Integration subscript question

1. Apr 27, 2013

### Intricacy

Simple Integration question

Hey: I am doing a practice exam question and it gives me two families of integrals, the first one being:

Cn= int(pi,0) xn cos(x) dx int n>= 0
It has asked for me to do integrate this as C0 I have assumed this means n = 0.
Do I change the n to a zero before or after integrating?

I can't find anywhere in my learning centre that tells me this. No urgency, this is just extra study for the exam in a few weeks. I may have additional questions that follow on this, but the integration itself seems straight forward, so do most of the future questions. Thanks in advance.

Last edited: Apr 27, 2013
2. Apr 27, 2013

### tiny-tim

Welcome to PF!

Hey Intricacy! Welcome to PF!
You mean Cn is defined as ∫0π xn cos(x) dx ?

Then C0 = ∫0π x0 cos(x) dx

3. Apr 27, 2013

### HomogenousCow

What does x underscript mean?

4. Apr 27, 2013

### Staff: Mentor

Writing an index as a subscript is a way to indicate multiple variables using only a single letter. For example, x0, x1, and x2 represent three different values.

Subscripts are often used to represent sequences of numbers or the coefficients of polynomials of arbitrary degree, as in p(x) = c0 + c1x + c2x2 + ... + cnxn.
Here the coefficients of the terms are the numbers {c0, c1, c2, ... , cn}.

$$C_n = \int_0^{\pi} x_n~cos(x)~dx \text{?}$$

Or do you mean
$$C_n = \int_0^{\pi} x^n~cos(x)~dx \text{?}$$

5. Apr 28, 2013

### Intricacy

Oh, I am so sorry for that. Yes I meant x^n, so sorry.

Thank you for that as well TinyTim. So I can turn the x^0 straight to 1 prior to integration?
Cn=∫π0 x^n cos(x) dx? ----> C0=∫π0 cos(x)

6. Apr 28, 2013

### tiny-tim

Hi Intricacy!
Yes … that's the definition of Co.

7. Apr 28, 2013

### Intricacy

Thank you Tiny-Tim. Sorry for the obviously stupid question :P.