Compute the iterated integral 2 V8-y2 8-r2-y2 2 sin(2y+ 2 )dzdxdy 0 Compute the iterated integral 2 V8-y2 8-r2-y2 2 sin(2y+ 2 )dzdxdy 0
4. For each of the following, compute the integral or show it doesn't exist: 2 1 (a) SR3 dV R3 1+x2 + y2 +22 (b) Sc (22+42 2dA where C = {(x,y) : x2 + y2 < 1} (c) Ss zvydA where S dA where S = {(x, y):1 < x,0 <y <} 1 9 9
Compute the integral of the vector field F(x, y, z) = (2x, 29, 42) over (1) = (cos(i), sin(i),1) for OSISK (Use symbolic notation and fractions where needed.) F. dr =
Consider the vector field F(x, y, z) = (z arctan(y2), 22 In(22 +1), 32) Let the surface S be the part of the sphere x2 + y2 + x2 = 4 that lies above the plane 2=1 and be oriented downwards. (a) Find the divergence of F. (b) Compute the flux integral SS. F . ñ ds.
Question 9 1 pts What is the solution to the integral foll V1 – 22 dx?
10. Rewrite the following integral using cylindrical coordinates. Do NOT evaluate. V 25-y2 Lolo /x²+42 uz dz dx dy **
. 1. (Indefinite Integrals; 33pts). (i) Find the integral 42² 3 (x +9)(x - 2)(1-9) fin) Use a suitable change of variables to find the integral tan(I) da. (in Use integration by parts to find the integral
Use Stokes' Theorem to evaluate the line integral $cF. dr, where F(x, y, z) = (-y+z)i + (x – z)j + (x – y)k. S is the surface z = V1 – 22 – y2, and C is the boundary of S with counterclockwise orientation (from above).
Question 22 1 pts Compute the path integral of F = (y,x) along the line segment starting at (1,0) and ending at (3,1).
Provide correct answer Evaluate the surface integral Slo(x2 + y2 +42 ) ds where S is the part of the cone z = 4 - Vx2 + y2 above the z = 0 plane. The surface integral equals 271.62.pl