MAC 2313 Midterm: MAC2313 F99 Test 3
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1 + x2 dy dx (2) (15 pts. ) Sketch the region in the xy-plane corresponding to the double iterated integral. Write the iterated integral as an iterated integral with the order of integration reversed. Let r be the triangular region in the xy-plane with vertices. Set up (do not integrate) a triple iterated integral for the volume of d. R is the region in the rst quadrant between the circles and between the lines x2 + y2 = 2, x2 + y2 = 4 y = 0, y = x. Sketch the graph of r. using a double iterated integral, nd the value of xy da. Find the surface area of the part of z = x2 + y2 below the plane z = 4. Let s be the solid region bounded by the paraboloid z = 11 x2 clude a sketch of the projection of s onto the xy-plane. The density function is (x, y, z) = ez x2.
