Question is Evaluate double integral over S and integrand is given by xy / squareroot of 1 +2x^2 dS where the surface is S = { (x,y,x^2 +y)} : 0 less than and equal to x less than and equal to y , x+y less than and equal to 1
according to what i have done is i have taken f:z- x^2 - y . then grad f =(-2x , -1 , -1 ) and modulous of grad f is square root of 2(1+2x^2) . Then shadow region in XY Plane is triangle bounded by Y Axis when drawing intersection of two functions y=x and x+y=1 . then using ordinary double integration answer comes out to be (squareroot of 2) divided by 48 ...
But my answer seems to be inconsistent with the book . So please check whether my solution is correct or not . thanks for help
