calculate-0-du-u-z-2-if-z-r-e-i-and-pi-lt-lt-pi- Tinku Tara June 3, 2023 Integration 0 Comments FacebookTweetPin Question Number 67539 by mathmax by abdo last updated on 28/Aug/19 calculate∫0∞du∣u+z∣2ifz=reiθand−π<θ<π Commented by ~ À ® @ 237 ~ last updated on 29/Aug/19 ∣u+z∣2=(u+z)(u+z_)I=1z−z_∫0∞(1u+z_−1u+z)du=12iIm(z)[ln(u+z_u+z)]0∞=12irsinθ[ln1−ln(e−i2θ)]=θrsinθ Commented by mathmax by abdo last updated on 29/Aug/19 thankyousir. Commented by mathmax by abdo last updated on 29/Aug/19 letI=∫0∞du∣u+z∣2⇒I=∫0∞du(u+z)(u+z−)=1z−z−∫0∞(1u+z−−1u+z)du=12i(rsinθ)[ln(u+z−u+z)]0+∞=12irsinθ×(−ln(z−z))wehave−ln(z−z)=ln(zz−)zz−=z2∣z∣2=r2e2iθr2=e2iθ⇒ln(zz−)=2iθ⇒I=12irsinθ×(2iθ)⇒I=θrsinθ. Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: n-1-1-n-2-k-2-k-Next Next post: Suppose-0-lt-b-a-Show-that-the-area-of-intersection-E-F-of-the-two-regions-defined-by-E-x-y-x-2-a-2-y-2-b-2-1-and-F-x-y-x-2-b-2-y-2-a-2-1-is-4absin-1-b-a-2-b-2- Leave a Reply Cancel replyYour email address will not be published.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.