0. In the Mathematica command Integrate[Sin[x y], {x,0,1}, {y,0,2}] which integral is done first, the x integral___ or the y integral____? (check one)
0. In the Mathematica command Integrate[Sin[x y], {x,0,1}, {y,0,2}] which integral is done first, the x integral___ or the y integral____? (check one)
1. (8 points). Calculate the area of the quadrilateral with vertices at (0,0), (4,2), (2,2), and (4,6) An explicit line integral or sum of line integrals equal to this area is:_________________________________ The area is: _______________________________
2. (8 points). Find the area of that part of the given surface which lies over the specified region: z = 8 x + 4 y; = is the region between y = x^2 and y = x^6.
3. (8 points). Let F(x,y,z) := (y + 1)i + (x+cos(y)) j
4. (8 points). In the cylindrical coordinate system, a spiral ramp can be defined by the equation z = theta/3, 0 2 theta 2 4 pi 0 < r 2 1