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1 10) (20 pts) Evaluate $. 22 +23+3 dz, C is the e ellipse * + y2 = 1
Problem 8. Evaluate Jo y' dz + 3zy dy, where C is the boundary of the semianmulan region D in the upper half-plane between the circles x2 + y2 = 1 and x2 + y-4. ANSWERS. Problem 8. Evaluate Jo y' dz + 3zy dy, where C is the boundary of the semianmulan region D in the upper half-plane between the circles x2 + y2 = 1 and x2 + y-4. ANSWERS.
1 Evaluate ; dz,Cistheellipse + y2 = 1 c 2:+7:+3
3. Consider the triple integral 2z sin(x2 + y2 +22 - 2x) dy da dz. Set up, but do not evaluate, an equivalent triple integral with the specified integration order. a) (6 pts) da dz dy b) (7 pts) dz dr de (Cylindrical Coordinates) c) (7 pts) dp do do (Spherical Coordinates)
j [3x2 +5y + i(x2-y2)] dz along (0,0) =x. |Evaluate
Identify the surface 4.x2 - y2 + 2z2 +4 = 0. Hyperboloid of one sheets Elliptic paraboloid Hyperbolic paraboloid None of the above or below Hyperboloid of two sheets Ellipsoid
4. (15 pts) Evaluate I = SSSR (x2 + y2 + z²) dV where R is the cylinder given by 4 < x2 + y2 +z? 59.
Evaluate the following integral in cylindrical coordinates. 5 125-x² 4 5 0 0 1+x2 + y2 dz dy dx
evaluate JJ. (< –Y) A. ) Integrate f(x, y, z) = x2 + y2 + 22 over the cylinder x2 + y2 < 2,-2 <2<3 (IL dx dy dz Feraluate
2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2. 2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2.