help me to sovle the part c clearly, I need to know bounded of that with...
For the lamina that occupies the region D bounded by the curves x = y2 – 2 and x = 2y + 6, and has a density function: p(x, y) = y + 4, find: a) the mass of the lamina; b) the moments of the lamina about x-axis and y-axis; c) the coordinates of the center of mass of the lamina.
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...
Please show full solutions so i can understand 3. (i) 3pl Set up iterated integrals for both orders of integration forev dA, where D is the region in the ry-plane bounded by y -,4, and z-0 (ii) [3p] Evaluate the double integral in part (i) of this question using the easier order of integration. (ii) [3pl Find the average of the function f(, y) yey over the region D. 3. (i) 3pl Set up iterated integrals for both orders of...
Can you do 3 and 6 Determine whether the following assertions are true or false 1. The double integral JJDy2dA, where D is the disk x2 +y2く1, is equal to π/3 2. The iterated integral J^S 4drdy is equal to 3. The center of mass of the triangular lamina that occupies the region D- 10 4. The triple integral of a function f over the solid tetrahedron with vertices (0,0,0), x < 3,0 < y < 3-2) and has a...
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)...
11. Consider the parabolic coordinate system (u, v) related to the Cartesian coordi- nates (r, y) by х — 2иv, y — u? — u? for (и, v) € [0, оо) х [0, оо) 1 u = 1, u 2' (a) Sketch in the ry-plane the curves given u = 2. Then sketch in 1 v = 1, v = 2. Shade in the region R the xy-plane the curves given v = 2' bounded by the curves given by...
Use polar coordinates to find the centroid of the following constant-density plane region The region bounded by the cardioid r4+4cos0. Set up the double integral that gives the mass of the region using polar coordinates. Use increasing limits of integration. Assume a density of 1 dr d0 (Type exact answers.) Set up the double integral that gives My the plate's first moment about the y-axis using polar coordinates. Use increasing limits of integration. Assume a density of M,-J J O...
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...
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...