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https/wwwmathudcom/Student/PlayerHomework aspolhomeworkid-38 2674&questionld-; Math 273, fal2016 Homework: MML15 (13.2) Score: 0.29 of 1 pt 7017 complete) 132.69setup & Solve Find the volume of the following woldNgon The solid above theregion R-Oay) 0sxs1.0sys3- bounded by the paraboloids 9X.y: and z 18-9 -y and the coordinate planes inthe fist octant (Useintegersor fractions forany numbers intheexpressions. The volume of the region is cubic units. Simplify your answer Type an integer ora faction III Vi I. (u) More Enter your answer the answer bor and then click Check Answer All parts showing 011816 307 PM Sare HW Score: 82.65%, 5.79 of7 pts EE Question Hep

Explanation / Answer

given 0<=x<=1, 0<=y<=3-3x

z =9x2+y2,z =18-9x2-y2

volume =[0 to 1][0 to 3-3x](18-9x2-y2)-(9x2+y2) dy dx

volume =[0 to 1][0 to 3-3x](18-18x2-2y2) dy dx

volume =[0 to 1][0 to 3-3x](18y-18yx2-(2/3)y3) dx

volume =[0 to 1](18(3-3x) -18(3-3x)x2-(2/3)(3-3x)3)-(18*0-18*0x2-(2/3)03) dx

volume =[0 to 1](54(1-x) -54(1-x)x2-18(1-x)3) dx

volume =[0 to 1](54(1-x) -54(x2-x3)-18(1-x)3) dx

volume =[0 to 1](54(-1/2)(1-x)2 -54((1/3)x3-(1/4)x4)+(18/4)(1-x)4)

volume =[0 to 1](-27(1-x)2 -54((1/3)x3-(1/4)x4)+(9/2)(1-x)4)

volume =(-27(1-1)2 -54((1/3)13-(1/4)14)+(9/2)(1-1)4) -(-27(1-0)2 -54((1/3)03-(1/4)04)+(9/2)(1-0)4)

volume =(0 -54(1/12)+0) -(-27 -0+(9/2))

volume = -(54/12) +27 -(9/2)

volume = -(9/2) +27 -(9/2)

volume = 27 -9

volume = 18 cubic units

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