question 1 Assignment 8 (Due on May 29) 1. Evaluate JLjEyz dV, where E is the region bounded by-Zy2 + 2a2-5 and the...
Use cylindrical coordinates to evaluate the triple integral ∭E √(x2+y2)dV where E is the solid bounded by the circular paraboloid z = 1-1(x2+y2) and the xy -plane.
5. Evaluate /// (y +z) dV where E is bounded by x = 0, y = 0, x2 + y2 + z2 = 1, and x2 + y2 + 2?" = 9. Use spherical coordinates. Answer must be exact values.
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.
Evaluate the triple integral. ∭E5xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded by the curves y = √x, y = 0, and x = 1
Multivariable Calculus M273 Section 15.3 Page 4 of 4 5. Evaluate the integrals (a) (1 Credit) e dV, where E ((, y, z) 10yS 1,0 S v,0 Szsv. (b) (1 Credit) /// У dV, where E lies under the plane z = x + 2y and above the region in the zy-plane bounded by the curves y- r2,y 0 and z1. Multivariable Calculus M273 Section 15.3 5. Evaluate the integrals. (a) (1 Credit)e V, where E- (r, y, 2) l0...
Evaluate the triple integral. 3z dV, where E is bounded by the cylinder y2 + z2 = 9 and the planes x = 0, y = 3x, and z = 0 in the first octant E
5. [P] Calculate the following integrals in cylindrical coordinates. where E is the region bounded by the paraboloid z 1 + z2 + y2 and the plane-5. where C is the region bounded by the cylinder y29, and the planes r 3. 0 and (c) III"Enderigh.handdby-,.ATandth.planryel where E is the region bounded by the cone y2 and the plane y 1.
(1 point) Evaluate the triple integral redV where E is the region bounded by the parabolic cylinder z 1-y2 and the planesz = 0, x = i, and x =-1. (1 point) Evaluate the triple integral redV where E is the region bounded by the parabolic cylinder z 1-y2 and the planesz = 0, x = i, and x =-1.
Use cylindrical coordinates to evaluate the triple integral J Vi +y2 dV, where E is the solid bounded by the circular paraboloid z 16 -1(z2 +y2) and the xy-plane.
Question3: Evaluate SSE (x - y)dv, where E is the region enclosed by z= x2 – 1, z = 1 - x2, y = 0, and y = 2.