Prоblem 1. (10 pоints) Evаluаte the dоuble integrаl ∫12∫01x2y dxdy{"version":"1.1","math":"∫12∫01x2y dxdy"}. Problem 2. (10 points) Evaluate the double integral ∫02∫01(x+2ey-3) dxdy{"version":"1.1","math":"∫02∫01(x+2ey-3) dxdy"}. Problem 3. (10 points) Evaluate the double integral ∫01∫2x3x(x+y2) dydx{"version":"1.1","math":"∫01∫2x3x(x+y2) dydx"}. Problem 4. (10 points) Evaluate the double integral ∬Dyx3+1 dA{"version":"1.1","math":"∬Dyx3+1 dA"} over the region D={(x,y) | 0≤y≤x≤3}{"version":"1.1","math":"D={(x,y) | 0≤y≤x≤3}"}. You don't need to simplify your final answer. Problem 5. (15 points) Find the volume of the region under the surface z=xy2{"version":"1.1","math":"z=xy2"} and above the area bounded by x=y2{"version":"1.1","math":"x=y2"} and x-3y=4{"version":"1.1","math":"x-3y=4"}. You don't need to simplify your final answer. Problem 6. (15 points) Use polar coordinates to evaluate the double integral ∬D(x+y) dA{"version":"1.1","math":"∬D(x+y) dA"} where D={(x,y) | 1≤x2+y2≤4, x≥0}{"version":"1.1","math":"D={(x,y) | 1≤x2+y2≤4, x≥0}"}. Problem 7. (15 points) Evaluate the triple integral ∫∫∫B(2x+3y2+4z3) dV{"version":"1.1","math":"∫∫∫B(2x+3y2+4z3) dV"} where B={(x,y,z) | 0≤x≤1, 0≤y≤2, 0≤z≤3}{"version":"1.1","math":"B={(x,y,z) | 0≤x≤1, 0≤y≤2, 0≤z≤3}"}. Problem 8. (15 points) Evaluate the triple integral ∫∫∫Eez dV{"version":"1.1","math":"∫∫∫Eez dV"} where E{"version":"1.1","math":"E"} is enclosed by the paraboloid z=3+x2+y2{"version":"1.1","math":"z=3+x2+y2"}, the cylinder x2+y2=1{"version":"1.1","math":"x2+y2=1"}, and the xy{"version":"1.1","math":"xy"}-plane. Once you are done, take photos of your handwritten work, convert it into a pdf, and then send your work to your instructor within ten minutes after you hit the submit button on the exam. You can either sent it to the instructor via D2L messages or to the following email address collier.gaiser@ccaurora.edu
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