Evaluate the following integral. SSS (xy + x2 + y2) dV; D = {(x,y,z): -55x55, -15ys1,...
Evaluate the following integral in spherical coordinates. SSS--(=y2 +22)3120v 3/2 dV; D is a ball of radius 5 D SSS - (x2 + y2 +22) >/?dv=E D (Type an exact answer, using a as needed.)
Evaluate SSS, (x² + y2 + z)ele?+y't??)? DV, where B is the unit ball: B={(x,y,z)/x² + y2 +2+ <1}
Evaluate the triple integral I=∭D(x2+y2)dV where D is the region inside the cone z=x2+y2−−−−−−√, below the plane z=2 and inside the first octant x≥0,y≥0,z≥0. A. I=0 B. I=(π/20)2^5 C. I=(π/10)2^5 D. I=π2^5 E. I=(π/40)^25
Evaluate the integral. 3. Sss (xz – yz)ds; where S is portion of the plane in R3 z = x + y + 2, that lies inside the cylinder x2 + y2 = 1.
10. Consider the integral (x + y + z) dV where D is the volume inside the sphere x2 + y2 + x2 = 9 and above the plane z = 1. (a) (3 marks) Express I as an iterated integral using Cartesian coordinates with the order of integration z, x and y. DO NOT EVALUATE THIS INTEGRAL. (b) (3 marks) Express I as an iterated integral using spherical coordinates with the order of integration p, 0, and 0. DO...
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.
2. Use cylindrical coordinates to solve the integral SSS (x2 + y2) dx dy dz D Z 2 Z = 2 z=Ż (x2 + y2) tor - y Х
(1 point) Use spherical coordinates to evaluate the triple integral dV, e-(x+y+z) E Vx2 + y2 + z2 where E is the region bounded by the spheres x² + y2 + z2 = 4 and x² + y2 + z2 16. Answer =
(1 point) Evaluate the triple integral I2(x2 +y2)dV where D is the region inside the parabolid z 4-x2-y2 and inside the first octant2 0, 0,z0 B. I 12 D. I E. I (1 point) Evaluate the triple integral I2(x2 +y2)dV where D is the region inside the parabolid z 4-x2-y2 and inside the first octant2 0, 0,z0 B. I 12 D. I E. I
Q1. Evaluate the line integral f (x2 + y2)dx + 2xydy by two methods a) directly, b) using Green's Theorem, where C consists of the arc of the parabola y = x2 from (0,0) to (2,4) and the line segments from (2,4) to (0,4) and from (0,4) to (0,0). [Answer: 0] Q2. Use Green's Theorem to evaluate the line integral $. F. dr or the work done by the force field F(x, y) = (3y - 4x)i +(4x - y)j...