0-sinxdx-x- Tinku Tara June 4, 2023 Integration 0 Comments FacebookTweetPin Question Number 27410 by math1967 last updated on 06/Jan/18 ∫∞0sinxdxx Commented by math1967 last updated on 07/Jan/18 Thankyousir Commented by abdo imad last updated on 06/Jan/18 letintroducethefonctionf(t)=∫0∞sinxxe−txdxwitht⩾0afterverifyingthatfisderivablewehavef′(t)=−∫0∞sinxe−txdx=−Im(∫0∞e(i−t)xdx)=−[1i−te(i−t)x]x=0x−>∝=1i−t=i+t−1−t2=−t1+t2−i1+t2⇒f′(t)=−11+t2⇒f(t)=λ−arctan(t)andduetofcontinue∃M>0//f(t)⩽M∫0∞e−txdx=t−>∝soMt−>0soλ=π2andf(t)=π2−arctan(t)∫0∞sinxx=f(0)=π2. Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: I-n-0-1-x-2n-1-1-x-2-dx-n-0-prove-that-n-0-2n-1-I-n-2-2nI-n-1-Next Next post: 1-x-sin-1-x-dx- Leave a Reply Cancel replyYour email address will not be published.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.