I have to integrate the function F(x,y)=x+y on the line segment x=t , y=1-t , z=0 from (0,1,0) to (1,0,0) .So what i did is think the line segment as a vector function(curve) σ(t)=(t,1-t,0) with domain A:[0,1] kai took the contour integral of F(σ(t))*||σ'(t)||dt from [0,1] an found sqr2.Is it right? Would it be wrong to think the integral of F(x) as the double integral of F(x) as 0<=x<=1, 0<=y<=1-x ?? I did both ways found different result so i think the way with the double integral is wrong but dont know why.
2026-03-28 22:37:42.1774737462
Integration Exercise.Help!
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So u mean if you do it like in your second case i.e
$$\int \int_R{ }F(x,y)dydx $$ where R is the region bounded as 0<=x<=1, 0<=y<=1-x.thats taking points from that 2-d region R and evaluating F over these points. Then thats wrong if you were asked to integrate the function F(x,y)=x+y on the line segment.