(1 point) Calculate the integral of f(x, y, z)-3x2 + 3уг + z6 over the curve c(t) (cost, sint, t)...
13. (10 points) (a): Find the line integral of f(x, y, z) = x+y+z over the straight-line segment from (1,2,3) to 0,-1,1). (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 >, 0<t<27.
Suppose C is a curve parametrized by r(t)=<cost,sint,1> and S is the portion of z=x^2+y^2 enclosed by C, located in the vector field F=<z,-x,y>. 25. Suppose C is the curve parametrized by F(t) = (cost, sint, 1) and S is the portion of z = x2 + y2 enclosed by C, located in the vector field F = (2, -,y). Verify Stokes' theorem. That is, find show they are, in fact, the same. fe dr and SIC (curl ) ñds...
Given the path C: x(t) = (cost, sint, t), 0<t<2n. Let f(t, y, z) = x2 + y2 + 22. Evaluate (12 pts) f(,y,z)ds.
:) 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
Evaluate the line integral f F dr for the vector field F(x, y, z) curve C parametrised by Vf (x, y, z) along the with tE [0, 2 r() -(Vt sin(2πt), t cos (2πi), ?) , Evaluate the line integral f F dr for the vector field F(x, y, z) curve C parametrised by Vf (x, y, z) along the with tE [0, 2 r() -(Vt sin(2πt), t cos (2πi), ?) ,
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)
(1 point) Evaluate the triple integral of f(x, y, z) = cos(x2 + y²) over the solid cylinder with height 2 and with base of radius 1 centered on the z axis at z = -2. Integral = 6pisin(4)
(3 + 2ry,12-3уг), 5. Find JeF . Tds, (et sin t, et cost),0 t where F(x,y) and C is given by r(t) - T. (3 + 2ry,12-3уг), 5. Find JeF . Tds, (et sin t, et cost),0 t where F(x,y) and C is given by r(t) - T.
9. Evaluate the “vector valued” line integral 1.Podr Fodr where F(x, y, z) = (x, y, zy) TT and C is given by r(t) = (sint, cost, t), with N » 4. u sta
MATLAB ONLY MATLAB ONLY MATLAB ONLY MATLAB ONLY (x(t), y(t)) (t - sint, 1- cost 1. (15 pts) Consider the parametrized curve 0,7] 2) (10pts) Calculate the length of (x(t), y(t)) from 0 to 7 1) (5pts) Plot the graph of parametrized curve on (x(t), y(t)) (t - sint, 1- cost 1. (15 pts) Consider the parametrized curve 0,7] 2) (10pts) Calculate the length of (x(t), y(t)) from 0 to 7 1) (5pts) Plot the graph of parametrized curve on