iii) Evaluate SD da over a spherical surface, a) if D = (2 + 16r2)2 and...
iii) Evaluate SD da over a spherical surface, a) if D = (2 + 16r2)2 and r = 2 in the xy plane. b) If D = 10cos Of forr 2 and 0 srs"/2
iii) Evaluate SD da over a spherical surface, a) if D = (2 + 16r2)2 and r = 2 in the xy plane. b) If D = 10cos Of for r = 2 and 0 sr="/2. iv) Verify the following identities: a) V (FA) = fVX A+ Vf A b) (f9) = fVg+gof c) V. (VX A) = 0 d) x (vf) = 0
Question 2: Evaluate SS xy dA where D is the triangle in the (x, y) plane bounded by the lines y=x, x-5 and y=2. [10 points)
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. f(xyz) = 4x, where S is the cylinder X + z2-25, 0 ys2 The value of the surface integral is (Type exact answers, using T as needed.) Find the area of the following surface using the given explicit description of the surface. The cone z2 = (x2 +y2) , for Oszs8 Set up the surface integral for the given function over the given surface S as a...
1. Evaluate the iterated integrals: x2+2x+y a. JR 3x+3y dA, R: 15x32,0 sys 1 (Hint: Simplify the integrand first.) b. S ey/*dA where R is the region in the xy-plane bounded between y = x2 and y = x over the interval 1sx52. c. So Sex Sx**2 x dydzdx
Problem 6 Using Stokes' Theorem, we equate F dr curl F dA. Find curl F- PreviousS us Problem ListNext Noting that the surface is given by (1 point) Calculate the circulation, Fdr7in z - 16-x2 - y2, find two ways, directly and using Stokes' Theorem. dA The vector field F = 6y1-6y and C is the boundary of S, the part of the surface dy dx With R giving the region in the xy-plane enclosed by the surface, this gives...
2. Flux calculations: Set up the double integral for Js F dA using cylindrical, spherical or shadow method as appropriate. (a) Sis defined by z2 +--4for-1SS3,oriented away from y-axis. F-3 (b) Sis given by z2 + y2 + z2-9and F-1n+zk. (c) S is the conical face -V+ over the region r S 2 on the zy-plane, oriented downwards.
2. Flux calculations: Set up the double integral for Js F dA using cylindrical, spherical or shadow method as appropriate. (a) Sis...
y, dA where D is the solid in Octa 2 +--4 and the plane y-i. Evaluate by the cylinder nt I bounded JJD
y, dA where D is the solid in Octa 2 +--4 and the plane y-i. Evaluate by the cylinder nt I bounded JJD
Evaluate (*V19x2 + 19y2 dA, where D is the shaded region enclosed by the lemniscate curve r = sin(20) in the figure. r2 = sin 20 0.5 os (Use symbolic notation and fractions where needed.) «V19x + 19da = 0 Use cylindrical coordinates to find the volume of the region bounded below by the plane z = 3 and above by the sphere x2 + y2 + 2 = 25. (Use symbolic notation and fractions where needed.) V =
The spherical surface r = 1 m, 2 m and 3 m carry surface charge densities of 20, -9 and 17. 2 nC/m2 respectively Calculate the electric flux leaving through the surface r 5 m а. Find electric flux density at P (1, -1, 2) b. Four charges are located at the vertices of a rectangular plane shown in Fig. Find the magnitude and direction of resultant force on Qı. The width of the plane is 5 cm and the...