find-the-value-of-integral-0-e-px-sin-qx-x-dx-with-p-gt-0-and-q-gt-0- Tinku Tara June 4, 2023 Integration 0 Comments FacebookTweetPin Question Number 35228 by abdo mathsup 649 cc last updated on 16/May/18 findthevalueofintegral∫0∞e−pxsin(qx)xdxwithp>0andq>0 Commented by abdo mathsup 649 cc last updated on 18/May/18 letputI=∫0∞e−pxsin(qx)xdxchanbgementx=tgiveI=∫0∞e−pt2sin(qt2)t2tdtI=2∫0∞e−pt2sin(qt2)dt=∫−∞+∞e−pt2sin(qt2)dt=Im(∫−∞+∞e−pt2+iqt2dt)but∫−∞+∞e−pt2+iqt2dt=∫−∞+∞e−(p−iq)t2dt=p−iqt=u∫−∞+∞e−u2dup−iq=πp−iqI=πp−iq Commented by abdo mathsup 649 cc last updated on 18/May/18 I=Im(πp−iq)butp−iq=p2+q2(pp2+q2−iqp2+q2)=reiθ⇒r=p2+q2andtanθ=−qp⇒θ=−arctan(qp)p−iq=reiθ2=(p2+q2)14e−i2arctan(qp)I=Im(π(p2+q2)−14ei2arctan(qp))I=π(p2+q2)−14sin(12arctan(qp)) Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: 1-calculate-f-a-0-pi-dx-a-sin-2-x-cos-2-x-with-a-gt-0-2-find-the-value-of-g-a-0-pi-sin-2-x-a-sin-2-x-cos-2-x-2-dx-Next Next post: find-the-value-of-integral-0-e-2-ia-2-t-2-dt-with-a-from-R-a-lt-1- Leave a Reply Cancel replyYour email address will not be published.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.