L{cos}{s) = /-stecos(at) dtU =cos(at)dve^(-st)dtdu-asin(at)duv = (-1/s)e^(-st)00(a/s)e^(-st)sin(at)dt-U =als*sin(at)dve^(-st)dtdu(a^2/s)*cos(at)dtv =(-1/s)e^(-st)00001/sa/s((-1/s)e^(-st)*sin(at))a?001/se^(-st)cos(at)dts2Notice that this last integral is the same as the integral we started with. Treat this like anequation and move the integral to the left hand side:1e-st cos(at) dt -Thereforestcos(at) dts/(a^2+s^2)||||

Answered: Image /qna-images/answer/fb5e9394-f569-4037-a64c-176fdeb49fea.jpg

00 L{cos}(s) = -st e cos(at) dt u cos(at) dv e^(-st)dt du = -asin(at)du v =| (-1/s)e^(-st) 00 (a/s)e^(-st)sin(at)dt - U = als*sin(at) dv e^(-st)dt du = (a^2/s)*cos(at)dt v = (-1/s)e^(-st) 00 00 1/s als(-1/s)e^(-st)*sin(at)) a? 00 1/s e^(-st)cos(at)dt 82 Notice that this last integral is the same as the integral we started with. Treat this like an equation and move the integral to the left hand side: 1 e-at cos(at) dt - Therefore Je-t cos(at) dt s/(a^2+s^2) || || ||

00 L{cos}(s) = -st e cos(at) dt u cos(at) dv e^(-st)dt du = -asin(at)du v =| (-1/s)e^(-st) 00 (a/s)e^(-st)sin(at)dt - U = alssin(at) dv e^(-st)dt du = (a^2/s)cos(at)dt v = (-1/s)e^(-st) 00 00 1/s als(-1/s)e^(-st)*sin(at)) a? 00 1/s e^(-st)cos(at)dt 82 Notice that this last integral is the same as the integral we started with. Treat this like an equation and move the integral to the left hand side: 1 e-at cos(at) dt - Therefore Je-t cos(at) dt s/(a^2+s^2) || || ||

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter58: Achievement Review—section Five

Section: Chapter Questions

Problem 30AR: Determine dimension x to 3 decimal places.

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