Use application Geogebra for plotting graphs.
QUESTION 4 YE is the solid region bounded above by the plane X + 3y +...
Use a change of variables to find the volume of the solid region lying below the surface -f(x, y) and above the plane region R x, y)xy)e- R: region bounded by the square with vertices (4, 0), (6, 2), (4, 4), (2, 2)
Use a change of variables to find the volume of the solid region lying below the surface -f(x, y) and above the plane region R x, y)xy)e- R: region bounded by the square with vertices (4, 0),...
Find the volume of the solid bounded above by the surface z = f(x,y) and below by the plane region R. f(x, y) = x2 + y2; R is the rectangle with vertices (0, 0), (9, 0), (9, 6), (0, 6) ( ) cu units
2. (13 points) Let E be the solid region bounded by the planes x = 0, y = 0, 2=0, and x+y+z=1. (a) Sketch E. (b) Set up the integral SSSe ex+y+z dV as a triple iterated integral. (c) Compute the integral.
Find y dV, where E is the solid bounded by the parabolic cylinder z = xand the planes y = 0 and 2 = 15 – 3y E
(1 point) Find the mass of the solid bounded by the xy-plane, yz-plane, z-plane, and the plane (z/8) 1, if the density of the solid is given by o(r, y, z) = x + 3y (r/2)(y/4) mass
1. Find the volume of the solid. Under the plane x +2y-z=0 And above the region bounded by y=x and y=x+.Using double integral.
1. Let E be the solid region bounded above by the sphere 4 = x2 + y2 + z2 and below by the plane y-z =-2. a. Generate a 3D picture of the region E using 3D graphing software. b. Write the integral J [ f(x,y,z)dVas an iterated integral (in rectangular coordinates) in two different ways - one with integration with respect to z first, and one with integration with respect to y first.
3 (6 pts) Let E be the region bounded by the surfaces z = 1 – y, y = VI, and z = 0. Set up the integral SSSE f(x, y, z)dV with respect to dxdydz, dzdydx, and dydzdx.
Question 7 10 pts Let V be the solid bounded above by the surface z = f(x, y) = 6 - 2x – 2y, and bounded below by the region R in xy-plane, where R is the triangle bounded by the x-axis, y = x, and x = 1. Find the volume of V. O O O O O
6. (12pts) Consider the solid that is above the xy-plane, bounded above by =/4-x-y and below by +y a. Sketch the solid formed by the given surfaces b. Set up in rectangular coordinates the triple integral that represents the yolume of the solid. Sketch the appropriate projection. Do NOT evaluate the integrals. (Hint: Let dV- d dy de) c. Set up in cylindrical coordinates the triple integral that represents the volume of the solid. Sketch the appropriate projection. Do NOT...