calculate-A-n-0-n-x-x-dx-and-lim-n-A-n- Tinku Tara June 4, 2023 Integration 0 Comments FacebookTweetPin Question Number 37895 by abdo mathsup 649 cc last updated on 19/Jun/18 calculateAn=∫0n(x−[x])dxandlimn→+∞An Answered by tanmay.chaudhury50@gmail.com last updated on 19/Jun/18 ∫01(x−[x])dx+∫14(x−[x]dx+∫49(x−[x]dx+…∫01(x−0)dx+∫14(x−1)dx+∫49(x−2)dx+..+−−∫(n−1)2(n)2(x−n−1)dx={12−o22+42−122+92−422+…+(n)2−(n−1)22+{0.(1−0)+(4−1)+2(9−4)+3(16−9)+…+((n−1(n−n+1)}=n2+(3+10+21+ Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: find-nature-of-the-serie-n-1-k-0-n-1-C-n-k-x-n-Next Next post: let-I-n-0-n-1-x-2x-1-2-dx-1-calculate-I-n-interms-of-n-2-find-lim-n-I-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Leave a Reply Cancel replyYour email address will not be published.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.
![calculate A_n =∫_0 ^n (x−[(√x)])dx and lim_(n→+∞) A_n](https://www.tinkutara.com/question/Q37895.png)
![∫_0 ^1 (x−[(√x) ])dx+∫_1 ^4 (x−[(√x) ]dx+∫_4 ^9 (x−[(√x) ] dx +... ∫_0 ^1 (x−0)dx+∫_1 ^4 (x−1)dx+∫_4 ^9 (x−2)dx+.. +−−∫_(((√(n−1))^ )^2 ) ^(((√n) )^2 ) (x−(√(n−1)) )dx ={((1^2 −o^2 )/2)+((4^2 −1^2 )/2)+((9^2 −4^2 )/2)+...+((((√n) )^2 −((√(n−1)) )^2 )/2) +{0.(1−0)+(4−1)+2(9−4)+3(16−9)+...+( ((√(n−1)) (n−n+1)} =(n/2)+(3+10+21+](https://www.tinkutara.com/question/Q37956.png)