SQT - Stupid Questions

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Is this the Stupid Questions Thread?

I'm doing integral of e^(-st) t sin(t)dt from 0 to inf

and I get -2s/((1 + s^2)^2)

But wolframalpha says the answer is the positive version: 2s/((1 + s^2)^2)

I can't see where I'm going wrong. Can someone post the step-by-step?

you probably just fucked up a negative somewhere. Maybe the - in (-st)

how are we supposed to know what you did wrong when you dont show us any of your work brainlet?

just take the Laplace transform of sin(t) and differciate with respect to s.
ta da
differentiation under the integral sign is ur best friend

Underated

Write an arbitrary vector in a basis of eigenvectors of M, then swap all the eigenvalues out with the maximal/minimal eigenvalue?

since M is real symmetric its diagonalizable with eigenvectors e1,..., en with eigenvalues c1,..,cn

write x = sum of aiei

then
x^T M x
=(sum aiei)^T M (sum aiei)
=(sum aiei)^T sum aiciei)
=sum ai^2ci

should be

>= sum ai^2 min{ci}

on the last line of course