Integration subscript question

[Intricacy]

Simple Integration question

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

C_n= int(pi,0) x_n 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.

 

[tiny-tim]

Welcome to PF!

Hey Intricacy! Welcome to PF!

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

C_n= int(pi,0) x_n 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.

You mean C_n is defined as ∫₀^π x_n cos(x) dx ?

Then C₀ = ∫₀^π x₀ cos(x) dx

 

[HomogenousCow]

What does x underscript mean?

 

[Mark44]

What does x underscript mean?

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 + ... + c_nxⁿ.
Here the coefficients of the terms are the numbers {c₀, c₁, c₂, ... , c_n}.

C_n= int(pi,0) x_n cos(x) _{dx int n>= 0}

This is confusing. As tiny-tim already asked, do you mean
$$C_n = \int_0^{\pi} x_n~cos(x)~dx \text{?}$$

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

It has asked for me to do integrate this as C₀ I have assumed this means n = 0.

 

[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)

 

[tiny-tim]

Hi Intricacy!

So I can turn the x^0 straight to 1 prior to integration?

Cn=∫π0 x^n cos(x) dx? ----> C0=∫π0 cos(x)

Yes … that's the definition of C_o.

 

[Intricacy]

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