Recent content by royblaze

Thanks, I managed to get it :D

Awesome Voko, thanks so much. You did an excellent job of leading me to my own conclusion. Thanks again! It would be nice if I could give you a +1 or something along those lines. Great help!

By turning the product of the cosines into a sum of cosines, then it becomes clear that the integral in question would be zero after evaluation, I believe.

In the m ≠ n case though, it is just a sum of ∏/2 terms. And any sum (negative or otherwise) of ∏/2 terms gives a term of ∏, which for sin = 0. So if n = 1000 or m = 12312412, the sine of A + B or A - B would still be zero, no?

Oh what the hell I'll just say it. Since any sum of A and B (negative sum or otherwise) gives an even number multiple of ∏, then the sin (A+B) and sin (A-B) terms would give zero.

I thought I got the proof, but I did not...

Ah! You mean the literal sine of the quantities A + B, A - B, right? So the sum of A and B are sums of (σ∏)/2, where σ is some constant made by the sum of two odd numbers. And the sum of any odd numbers is an even number. Which puts the A + B into the form of just σ∏. Sine of a multiple of...

Right, okay, so if m = n, then the cosine term immediately becomes cos(0) = 1, and the integral of 1 in this case would just be the variable x. But why are we considering m = n? As for the second question... I guess that A+B would be a positive number and A-B would be a negative number? In...

Andrien, perhaps you can assist in my integration? I am a little confused. My sum (after subtraction as you suggested): XnX"m + λmXmXn - XmX"n - λnXnXm I tried to integrate term by term but I am getting very confused by the multiple instances of integration by parts. When can I stop...

For the integration from 0 to 1, for (a+b) and (a-b) respectively I get: sin(a+b)/(a+b) sin(a-b)/(a-b) Since it is basically a sum of integrals, I can just sum these (with the accompanying 1/2), correct? But I don't know what else after that: this is where I got confused.

Voko, I used the characteristic equation of the differential equation, and using Euler's formula as the general form of the homogenous equation, I solved three different cases based on the sign of λ. The negative and zero case for λ gives trivial solutions of X = 0. Only the positive case gives...

I believe it is sin(ax)/a evaluated from 0 to 1, so that would be sin(a)/a, correct?

Homework Statement For the following diff. eqns (fcns of t) X''m + λmXm=0 Xm (1)=0 X'm=0 X''n + λnXn=0 Xn (1)=0 X'n=0 Show that ∫XmXndt from 0 to 1 equals 0 for m≠n. Homework Equations Qualitative differential equations... no idea really what to put in this section. The...

Homework Statement Show that (forgive me for not knowing how to use latex) from x=0 to x=1 of: ∫cos([(2n+1)(pi)/2]x)*cos([(2m+1)(pi)/2)]x) dx = 0, for m ≠ n Homework Equations The question tells me to use integral tables. The Attempt at a Solution Using integral tables, I got...

I have solved the question after clarifying some assumptions that were not given to us.