let-C-x-y-R-2-0-x-1-and-y-2x-2-calculate-C-x-2-ydx-x-2-y-2-dy- Tinku Tara June 4, 2023 Integration 0 Comments FacebookTweetPin Question Number 36195 by prof Abdo imad last updated on 30/May/18 letC={(x,y)∈R2/0⩽x⩽1andy=2x2}calculate∫Cx2ydx+(x2−y2)dy Commented by math khazana by abdo last updated on 18/Aug/18 ∫Cx2ydx+(x2−y2)dy=∫Cx2(2x2)dx+∫C(x2−4x4)(4x)dx=∫014x4dx+4∫01(x3−4x5)dx=45[x5]01+4[x44−23x6]01=45+4{14−23}=45+1−83=95−83=27−4015=−1315. Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: let-D-x-y-z-R-2-0-lt-z-lt-1-and-x-2-y-2-lt-z-2-calculate-D-xyzdxdydz-Next Next post: let-gt-0-and-C-the-circle-x-2-y-2-2-calculate-C-ydx-xy-dy- Leave a Reply Cancel replyYour email address will not be published.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.
![∫_C x^2 ydx +(x^2 −y^2 )dy =∫_C x^2 (2x^2 )dx +∫_C (x^2 −4x^4 )(4x)dx =∫_0 ^1 4x^4 dx + 4∫_0 ^1 (x^3 −4x^5 )dx =(4/5)[x^5 ]_0 ^1 + 4 [ (x^4 /4) −(2/3) x^6 ]_0 ^1 =(4/5) +4{(1/4) −(2/3)} =(4/5) +1 −(8/3) = (9/5) −(8/3) =((27−40)/(15)) =−((13)/(15)) .](https://www.tinkutara.com/question/Q42104.png)