How is integral finished? and what integral equation used?

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zqz51911
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Equation: a_n = integral of psi_n* F dtau = (2/l)^(1/2) times integral from 0 to l of (sin(n pi x / l)) x(l - x) dx = (2^(3/2) l^(5/2)) / (n^3 pi^3) times [1 - (-1)^n]
 
Hello zq,
Is there a context to this question ? What is this about ? Any idea what each of the various symbols stands for ?
 
sorry for the so simple description
this is a expand F(x) with particle in a box energy eigenfuctions
F(x)=x(x-l) for 0<x<l and F(x)=0 elsewhere
psi is the wave function of ground state particle in a box equation
 
So at the core you need $$ \int_0^l x\, sin(ax)\; dx {\rm \quad and \quad} \int_0^l x^2 \,sin(ax)\; dx$$ (with ## a = n\pi/l##) , right ?
Ever met these integrals ?
 
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BvU said:
So at the core you need $$ \int_0^l x\, sin(ax)\; dx {\rm \quad and \quad} \int_0^l x^2 \,sin(ax)\; dx$$ (with ## a = n\pi/l##) , right ?
Ever met these integrals ?
thanks,