calculate-0-x-2-cos-pix-x-2-4-2-dx- Tinku Tara June 4, 2023 Integration 0 Comments FacebookTweetPin Question Number 38724 by maxmathsup by imad last updated on 28/Jun/18 calculate∫0∞x2cos(πx)(x2+4)2dx Commented by maxmathsup by imad last updated on 30/Jun/18 letI=∫0∞x2cos(πx)(x2+4)2dx2I=∫−∞+∞x2cos(πx)(x2+4)2dx=Re(∫−∞+∞x2eiπx(x2+4)2)letφ(z)=z2eiπz(z2+4)2wehaveφ(z)=z2eiπz(z−2i)2(z+2i)2sothepolesofφare2iand−2i∫−∞+∞φ(z)dz=2iπRes(φ,2i)butRes(φ,2i)=limz→2i1(2−1)!{(z−2i)2φ(z)}(1)=limz→2i{z2eiπz(z+2i)2}(1)=limz→2i{(2zeiπz+iπz2eiπz)(z+2i)2−2(z+2i)z2eiπz(z+2i)4}limz→2i(2z+iπz2)eiπz(z+2i)−2z2eiπz(z+2i)3=(4i−4iπ)e−2π(4i)+8e−2π(4i)3=(−16+16π+8)e−2π−64i=(8−16π)e−2π64i∫−∞+∞φ(z)dz=2iπ(8−16π)e−2π64i=π(8−16π)e−2π32=π328(1−2π)e−2π=π4(1−2π)e−2π⇒ Commented by maxmathsup by imad last updated on 30/Jun/18 2I=π4(1−2π)e−2π⇒I=π8(1−2π)e−2π.π Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: let-f-x-x-1-e-x-and-g-x-ln-2-x-2-1-calculate-fog-x-and-gof-x-2-calculate-fog-x-and-gof-x-Next Next post: log-e-e-2-x-lnx-log-e-x-3-faind-x- Leave a Reply Cancel replyYour email address will not be published.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.