calculate-U-n-1-n-n-2-x-2-y-2-e-x-2-y-2-dxdy-and-lim-n-U-n- Tinku Tara June 4, 2023 Integration 0 Comments FacebookTweetPin Question Number 110451 by mathmax by abdo last updated on 29/Aug/20 calculateUn=∫[1n,n[2(x2−y2)e−x2−y2dxdyandlimn→+∞Un Answered by mathmax by abdo last updated on 31/Aug/20 weconsiderthediffeomorphism{x=rcosθy=rsinθ0⩽x<nand0⩽y<n⇒0⩽x2+y2<2n2⇒0⩽r2<2n2⇒0⩽r<n2⇒Un=∫∫0⩽r<n2and0⩽θ⩽π2r2(cos2θ−sin2θ)e−r2rdrdθ=∫0n2r3e−r2dr.∫0π2cos(2θ)dθbut∫0π2cos(2θ)dθ=[12sin(2θ)]0π2=0⇒Un=0∀n⇒limUn=0 Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: please-calculate-I-0-pi-2-dx-1-tanx-2-J-0-pi-dx-a-2-cos-2-x-sin-2-x-K-0-pi-2-dx-3tanx-2-Next Next post: find-0-1-2-ln-x-2-3y-2-e-x-2-3y-2-dxdy- Leave a Reply Cancel replyYour email address will not be published.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.