JedV Evaluate E , where E is enclosed by the paraboloid :=x+ y and the plane...
Use cylindrical coordinates. Evaluate the integral, where E is enclosed by the paraboloid z = 3 + x2 + y2, the cylinder x2 + y2 = 6, and the xy-plane. e dy
Evaluate the triple integral below where E is enclosed by the paraboloid 2= 4 - - y2 and 2 = -2. SIJ. 20 zdV
Evaluate the triple integral. SSS E 8x dV, where E is bounded by the paraboloid x = 5y^2 + 5z^2 and the plane x = 5.
Question3: Evaluate SSE (x - y)dv, where E is the region enclosed by z= x2 – 1, z = 1 - x2, y = 0, and y = 2.
Problem 3 (8 marks) Evaluate the surface integral JJz"(x+y*)dS , where S s the part of the plane z 3 inside the paraboloid z = x2 + y2.
Problem 3 (8 marks) Evaluate the surface integral JJz"(x+y*)dS , where S s the part of the plane z 3 inside the paraboloid z = x2 + y2.
1. (6 marks) Find the volume of the solid enclosed by the paraboloid 2 = 1 - 22 - y2 and the coordinate planes of the first octant O = {(x, y, z) | x > 0, y > 0, z>0}. 2. (7 marks) Calculate SS/ (82 +93) dr dy dz. where E is the upper hemisphere x2 + y2 + 22 < 1 and 2 > 0. 3. (7 marks) Evaluate the integral SL (x + y) er?-y dA...
Evaluate the triple integral ∭ExdV where E is the solid bounded by the paraboloid x = 5y2 + 5z2 and x = 5.
2. (a) Let R be the solid enclosed by the paraboloid 2 = 8 - (x + ) and the cone 2=2V12+ ye. Find the volume of R. (b) Let E be the region lying between the upper hemispheres r2 + y2 + 2 = 4,:> 0 and r2 + y2 + 3) = 9,320. Evaluate I[] vFP+$2V
5. Evaluate the integral: (x) dedrdy, where B is the cylinder over the rectangular region R-(, y) ER21,-2S of the ay plane, bounded below by the surface 1os y and above by the sur face of elliptical paraboloid 22 2- 2)
5. Evaluate the integral: (x) dedrdy, where B is the cylinder over the rectangular region R-(, y) ER21,-2S of the ay plane, bounded below by the surface 1os y and above by the sur face of elliptical paraboloid 22...
Find the volume of the solid enclosed by the paraboloid z = 4 + x^2 + (y − 2)^2 and the planes z = 1, x = −3, x = 3, y = 0, and y = 3.