Having trouble with this problem. f(x) = e^-x*cos(x) x>= 0. Have to find the Fourier Sine and Cosine integral representations. Ok so I know to setup the intergral as
Intregral(0, inf) of e^-t*cos(t)*cos(w*t)dt and I know I need to use integration by parts but since the derivative of e^-t is just -e^-t and derivative of cos(t) is sin(t) the intergration of parts will never stop... I just keep getting e^-t, cosine and sine terms. Also I am not sure how the 2nd cosine term would be used in the integration by parts. Would I do e^-t*cos(t) by itself then use the answer to that to integrate cos(w*t)???
Thanks if you can help...
Intregral(0, inf) of e^-t*cos(t)*cos(w*t)dt and I know I need to use integration by parts but since the derivative of e^-t is just -e^-t and derivative of cos(t) is sin(t) the intergration of parts will never stop... I just keep getting e^-t, cosine and sine terms. Also I am not sure how the 2nd cosine term would be used in the integration by parts. Would I do e^-t*cos(t) by itself then use the answer to that to integrate cos(w*t)???
Thanks if you can help...