Math 208 - Quiz 7 - Due October 19, 2016 Name: ____________________________ Attach separate sheets of neat solutions to the following problems. Please staple sheets together. Neatness and good communication count. 1. (4 points) Evaluate R 3 x y2 dA , where R : 0 x 8, 1 y 4 . Write your answer in exact form, not a decimal approximation. 2. 3. For the double integral 2 1 y9 3 0 0 ( ) x 2 + ye x dx dy : (a) (2 points) Sketch the region of integration. (b) (3 points) Write, BUT DO NOT EVALUATE, an equivalent double integral with the order of integration reversed. (4 points) Evaluate 1 y! 0 0 1 1x 2 0 0 3 $ ## & dx dy . Write your answer in exact form, not a decimal 2& "4+ y % approximation. 4. (6 points) Evaluate 4x 2 y 3 ( x ) dz dy dx . Write your answer in exact form, not a decimal approximation. 5. (6 points) Set up, BUT DO NOT EVALUATE, a triple integral that will find the mass of a solid cut from the cylinder x 2 + y 2 = 4 by the planes x + z = 3 and y + z = 10 that has a density given by ( x, y,z) = cos( xyz) g/cm3.