calculate-0-x-e-x-2-a-2-sin-bx-dx-with-a-gt-0-and-b-gt-0- Tinku Tara June 4, 2023 Integration 0 Comments FacebookTweetPin Question Number 63214 by mathmax by abdo last updated on 30/Jun/19 calculate∫0∞xe−x2a2sin(bx)dxwitha>0andb>0 Commented by mathmax by abdo last updated on 01/Jul/19 letI=∫0∞xe−x2a2sin(bx)dx⇒2I=∫−∞+∞xe−x2a2sin(bx)dxbypartsu′=xe−x2a2andv=sin(bx)⇒2I=[−a22e−x2a2sin(bx)]−∞+∞−∫−∞+∞−a22e−x2a2bcos(bx)dx=a2b2∫−∞+∞e−x2a2cos(bx)dxletdetermineAλ=∫−∞+∞e−λx2cos(bx)dxwithλ>0Aλ=Re(∫−∞+∞e−λx2+ibxdx)∫−∞+∞e−λx2+ibxdx=∫−∞+∞e−{(λx)2−2λxib2λ−b24λ+b24λ}dx=∫−∞+∞e−(λx+ib2λ)2e−b24λdx=λx+ib2υ=ue−b24λ∫−∞+∞e−u2duλ=πλ⇒Aλ=πλe−b24λ⇒2I=a2b2πλe−b24λandλ=1a2⇒I=a2b4π1ae−b241a2=π4a3be−a2b24 Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Question-128745Next Next post: Find-maximum-value-of-x-16-y-2-y-4-x-2-for-all-real-x-and-y- Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.