40 1. 16 pts) Evaluate the integral( quadrant enclosed by the cirle x + y2-9 and the lines y - 0 ...
1) a.(20 pts) Set up the integral corresponding to the volume of the solid bounded above by the sphere x2+y2 + z2 16 and below by the cone z2 -3x2 + 3y2 and x 2 0 and y 20. You may want to graph the region. b. (30 pts) Now find the mass of the solid in part a if the density of the solid is proportional to the distance that the z-coordinate is from the origin. Look at pg...
6. (20 points) Find the centroid of the region in the first quadrant bounded by the z-axis. 1-y2, and the line x + y 2. 6. (20 points) Find the centroid of the region in the first quadrant bounded by the z-axis. 1-y2, and the line x + y 2.
Hi, I need help solving number 13. Please show all the steps, thank you. :) Consider the solid Q bounded by z-2-y2;z-tx at each point Р (x, y, z) is given by mass of Q [15 pts] 9. x-4. The density Z/m 3 . Find the center of (x, y, z) [15 pts] 10. Evaluate the following integral: ee' dy dzdx [15 pts] 11. Use spherical coordinates to find the mass m of a solid Q that lies between the...
5) Given the function fix.y) - x2 and region R bounded by x 0, y x and 2x+y 6 (a) Sketch the region R (label lines, intercepts, axes and shade region) (b) SET UP the integral over this region (c) Assuming f(x.y)- xa is the density function for the lamina R given above, determine the mass for R 5) Given the function fix.y) - x2 and region R bounded by x 0, y x and 2x+y 6 (a) Sketch the...
1. Find the mass and centroid of the region bounded by the = y2 with p (a, y) parabolas y x2 and x 2. Set up the iterated (double) integral(s) needed to calculate the surface area of the portion of z 4 2 that is above the region {(«, у) | 2, x < y4} R 2 Perform the first integration in order to reduce the double integral into a single integral. Use a calculator to numerically evaluate the single...
6. (4 pts) Consider the double integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a) Sketch the region of integration R in Figure 3.(b) By completing the limits and integrand, set up (without evaluating) the integral in polar coordinates.∫R(x2+y)dA=∫∫drdθ.7. (5 pts) By completing the limits and integrand, set up (without evaluating) an iterated inte-gral which represents the volume of the ice cream cone bounded by the cone z=√x2+y2andthe hemisphere z=√8−x2−y2using(a) Cartesian coordinates.volume =∫∫∫dz dxdy.(b) polar coordinates.volume =∫∫drdθ. -1 -2 FIGURE 3. Figure for Problem 6. 6. (4 pts)...
6. (4 pts) Consider the double integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a) Sketch the region of integrationRin Figure 3.(b) By completing the limits and integrand, set up (without evaluating) the integral in polar coordinates. -1 -2 FIGURE 3. Figure for Problem 6. 6. (4 pts) Consider the double integral V2 /2-y² + = (x2 + y) dx dy + + y) do dy. 2-y2 (a) Sketch the region of integration R in Figure 3. (b) By completing the limits and integrand, set up (without evaluating)...
Math23 2 Consider the region in first quadrant area bounded by y x, x 6, and the x-axis. Revolve this bounded region about the x-axis a) Sketch this region and find the volume of the solid of revolution; use the disk method and show an element of the volume. (15 marks) b) Find the coordinates of the centroid of the solid of revolution. c) Find the coordinates of the centroid of the plate; on the sketch above, show the vertical...
9. The region bounded by y = x2, y = 3x, is revolved about the x-axis. a) Sketch the region b) Sketch the solid and a representative disk/washer. c) Set-up the integral to find the volume using disks/washers. DO NOT SOLVE!!!
Math232 2 Consider the region in first quadrant area bounded by y x,x=6, and the x-axis. Revolve this bounded region about the x-axis a) Sketch this region and find the volume of the solid of revolution; use the disk method, and show an element of the volume. (15 marks) b) Find the coordinates of the centroid of the solid of revolution Find the moment of inertia of the solid of revolution with respect to the x-axis. d) Math232 2 Consider...