A= 30.30
6. Find the area of the portion of the surface x.))4 that lies above the region...
11. Find the area of the portion of the surface f(x, y) 1-x2+ y that lies above the triangular region with vertices (1, 0, 0), (0, -1, 0) and (0, 1, 0). 11. Find the area of the portion of the surface f(x, y) 1-x2+ y that lies above the triangular region with vertices (1, 0, 0), (0, -1, 0) and (0, 1, 0).
2. Find the surface area of the portion of the paraboloid z = /16-x? - y2 that lies between the cylinders x² + y2 =1 and x² + y2 =4. (you may use fnint as needed)
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...
Solve c and d Please. Find the area of the following surfaces. a) The part of the plane 3z + 2y +z 6 that lies in the first octant. b) The part of the cone zVy that lies between the plane y z and the cylinder y-x c) The surface with vector equation r(u, u) = (u . cos(v), u . sin(v), u) , where 0 u 1, 0 v S T. d) The portion of the unit sphere that...
10. (a) Find the surface area of the portion of the graph of f(x, y)-yx which is above the region in the xy- plane bounded by y x,y 0 and x.(b) Let f(x)-2 (n+3)2 _____ for each x for which the series o 5" converges. Write a power series in summation notation for an indefinite integral of f. 10. (a) Find the surface area of the portion of the graph of f(x, y)-yx which is above the region in the...
z-(x, y)over the region R. 9. Find the area of the surface given by.y)over the region R. f(x, y)--3-4x +2y R: square with vertices (0, 0), (5, 0), (5, 5), (o, 5)
Evaluate the integral: dzdrdy where B is the cylinder over the rectangular region R {(x,y) E R2:-1 1,-2y2) sin z sy and above by the sr of the , bounded ethe surface 12 уг 2- face of elliptical paraboloid 37 42081 Evaluate the integral: dzdrdy where B is the cylinder over the rectangular region R {(x,y) E R2:-1 1,-2y2) sin z sy and above by the sr of the , bounded ethe surface 12 уг 2- face of elliptical paraboloid...
5. Calculate the surface area of the portion of the sphere x2+y2+12-4 between the planes z-1 and z ะไ 6. Evaluate (xyz) dS, where S is the portion of the plane 2x+2y+z-2 that lies in the first octant. 7. Evaluate F. ds. a) F = yli + xzj-k through the cone z = VF+ア0s z 4 with normal pointing away from the z-axis. b) F-yi+xj+ek where S is the portion of the cylinder+y9, 0szs3, 0s r and O s y...
Find the area of the surface given by z = f(x, y) over the region R. (Hint: Some of the integrals are simpler in polar coordinates.) f(x, y) = x2 + y2, R = {(x, y): 0 = f(x,y) 3}
6) a) Find the area of the circle (x-3)+ y'- 9 using polar coordinates b) Find the area of the region below the cardioid r = 1 + cos(9) and above y = 1x1. 6) a) Find the area of the circle (x-3)+ y'- 9 using polar coordinates b) Find the area of the region below the cardioid r = 1 + cos(9) and above y = 1x1.