Problem 1. (10 points) Evaluate the double integral ∫12∫01x…
Problem 1. (10 points) Evaluate the double integral ∫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, please take pictures of your work, convert them into a pdf file; then scroll down to the bottom of this page to upload your file by clicking on “Add a File”. Finally, please click “Submit Quiz.” If you have trouble opening your file on your computer during the exam, you can also email your file to your instructor within 10 minutes after you submit your exam. Your instructor’s email address is collier.gaiser@ccaurora.edu
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