Question 2 (25 points): Use triple integration in Cartesian coordinates to find the center of mass for the solid in the first octant bounded by the (XY, YZ, ZX) planes, and the surface z =4-x²-y, as shown in the figure? Use 5(x,y) = 15 Z-4-x-y

a) Find a vector parametric equation for the ellipse that lies on the plane y - 4x + z = -8 and inside the cylinder y = 4. x2 + r(u, v) = for 0 < u < 2 and 0 < v < 2n. (6) aA = 7, x, = X. (c) dA = usqrt3 (d) Set up and evaluate a double integral for the surface area of the ellipse. Surface area =

Let F = -9zi+ (xe#z– 2xe**)}+ 12 k. Find f, F·dĀ, and let S be the portion of the plane 2x + 3z = 6 that lies in the first octant such that 0 < y< 4 (see figure to the right), oriented upward. Z Explain why the formula F · A cannot be used to find the flux of F through the surface S. Please be specific and use a complete sentence.

Use quadrilateral JKLO. yK -2 0 -2 !3D What are the coordinates of the image R(90 o)(JKLO) = J'K'L'O'? J = ( K' = ( L' ( O = ( Review pro 2.