How to prove the equation for sum of cubes

[goodness52200]

http://xs305.xs.to/xs305/06332/ss.gif

Hello all, how to prove the above equation
thanks a lot

 

[VietDao29]

Could you explain what $$s, \sigma , \ j, \ \omega$$ are? Are they constants, negative or positive?

 

[goodness52200]

hi ViettDao29
s is a complex

 

[yenchin]

Oh... so j is our usual i=sqrt(-1)
Use an inequality for integral that absolute value of integral is less than or equal to integral of absolute value. Then consider that

$$|e^{-s}| = |e^{- \sigma}| |e^{-j \omega}|<br />$$

Now, what is $|e^{-j \omega}|$ ?

 

[benorin]

Also recall that $$\, \left| \int f(x) \, dx\right| \leq \int\left| f(x) \right| \, dx$$