calculate-0-2pi-cos-5-3cos-d- Tinku Tara June 4, 2023 Integration 0 Comments FacebookTweetPin Question Number 64649 by mathmax by abdo last updated on 20/Jul/19 calculate∫02πcosθ5+3cosθdθ Commented by mathmax by abdo last updated on 20/Jul/19 letA=∫02πcosθ5+3cosθ⇒A=13∫02π3cosθ+5−53cosθ+5dθ=2π3−53∫02πdθ3cosθ+5changementeiθ=zgive∫02πdθ3cosθ+5=∫∣z∣=113z+z−12+5dziz=∫∣z∣=12dziz(3z+3z−1+10)=∫∣z∣=1−2i3z2+3+10zdzletW(z)=−2i3z2+10z+3polesofW?Δ′=52−9=16⇒z1=−5+43=−13andz2=−5−43=−3⇒W(z)=−2i3(z−z1)(z−z2)(z2isoutofcircle)residustheoremgive∫∣z∣=1W(z)dz=2iπRes(W,z1)Res(W,z1)=limz→z1(z−z1)W(z)=−2i3(z1−z2)=−2i3(−13+3)=−2i3.83=−i4⇒∫∣z∣=1W(z)dz=2iπ(−i4)=π2⇒A=2π3−53π2=2π3−5π6=4π−5π6⇒A=−π6. Answered by MJS last updated on 20/Jul/19 ∫2π0cosθ5+3cosθdθ=2∫π0cosθ5+3cosθdθ=[t=tanθ2→dθ=2cos2θ2dt]−2∫∞0t2−1(t2+1)(t2+4)dt=43∫∞0dtt2+1−103∫∞0dtt2+4==[43arctant−53arctant2]0∞=−π6 Commented by mathmax by abdo last updated on 20/Jul/19 thankyousir. Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Question-130181Next Next post: U-n-is-a-sequence-wich-verify-lim-n-U-n-1-U-n-a-calculate-lim-n-U-n-n- Leave a Reply Cancel replyYour email address will not be published.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.