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3. Given the function z = f(x,y) = y2 xy + x + 20: a. Find the volume of the solid bounded by the xy plane and the surface of the function over the rectangle {(x, y)| 1 S x S 1, 0 S y S 3}. Use either order of integration. Use the other order to make sure the correct value is found. (4) b. Set up, but don't evaluate yet, the double integrals for computing the volume bounded by the xy plane and the surface of the function over the triangulaI sub region of the above rectangle, as shown in the graph. (3) 3 continued. Given the function z = f (x, y) = y2 xy + x + 20: 6. Use one order of integration (one is easier than the other) to find the volume bounded by the .132 plane and the surface of the function over the triangular sub-region of the above rectangle, as shown in the graph (same as in part b). (3) (1. Find the volume bounded by the xy plane and the surface of the function over the other triangular sub-region (see graph) in the simplest way, without using direct integration. Also, produce the result by integrating explicitly. (4)