1. Find (2.rº + y) DV where Q = { (z,y,z) | 0<<<3, -2<y<1, 1<2<2} 1 / 12
Evaluate SSS, (x² + y2 + z)ele?+y't??)? DV, where B is the unit ball: B={(x,y,z)/x² + y2 +2+ <1}
Question 3 1 pts Calculate Sw y DV using cylindrical coordinates, where W is the solid: z? + y2 < 4, 2 > 0 y 0, 0 <z<6.
(9) Stokes' Theorem for Work in Space F(x, y, z) =< P,Q,R >=<-y+z, x - 2,x - y > S:z = 4 - x2 - y2 and z>0 (9a) Evaluate W= $ Pdx + Qdy + Rdz с (9) Stokes' Theorem for Work in Space F(x, y, z) =< P,Q,R>=<-y+z, x - 2, x - y > S:z = 4 - x2 - y2 and z 20 (9b) Verify Stokes' Theorem.
(8) The Divergence Theorem for Flux in Space F(x, y, z) =< P, Q, R >=< xz, yz, 222 > S: Bounded by z = 4 – x² - y2 and z = 0 Flux =S} F înds S (8a) Find the Flux of the vector field F through this closed surface. (8) The Divergence Theorem for Flux in Space F(x,y,z) =< P,Q,R >=< xz, yz, 222 > S: Bounded by z = 4 – x2 - y2 and z...
:) IS (x+y+z)ds X-1 (b): Find the work done by F over the curve in the direction of increasing t, where F =< x² + y, y2 + 1, ze >, r(t) =< cost, sint,t/27 >, Osts 27. y-2=2-3 =+ C) -1-2 I-3
c(x + y2) for 0 SX S1 and 0 sys1 f(x,y) = 0 0.w. Find the conditional pdf of X given Y = y. (a) (b) Fim (r< 10-1)
12xz dV, where S is the solid region in the first octant (x, y, z > 0) that lies above the parabolic cylinder z = y2 and below the paraboloid Evaluate the triple integral I = 1] 1222 dV, where S ist 2= 8 – 2x2 - y2.
Use spherical coordinates to calculate the triple integral of f(x, y, z) = y over the region x2 + y2 + z2 < 3, x, y, z < 0. (Use symbolic notation and fractions where needed.) S S lw y DV = help (fractions)
dV, where is the unit ball in R3, that is, Use spherical coordinates to compute the integral We E = {(x, y, z)| 22 + y2 + 2 <1}.