Recent content by sgupta31

and for part c) sphere I am using (x^2)+ (y^2) + (z^2)<= (4*(a^2)) which means that the vector r(theta, phi)=2asintheta cosphi i+2a sinphi sintheta j+ 2a cosphi k where 0<theta< 2 pi and 0<phi<pi. I am not sure but finding vector n and F(r(theta,phi)). r'(theta,phi) seems very ugly and complex...

Thank you so much Vela. So I understand why the limits were taken to be negative, as we were calculating all the area (ie. below the z=0 plane as well). I got an answer of 12*sqrt(3)*pi*(a^3). Since there is an (a^3) I feel its about right, for a volume. Now for part b) Surface S_1...

Thanks. So I took the lower limit of z to be -(4*(a^2)-(r^2)) and the integral I get using Divergence theorem ie. I multiply the integral by divF=3. I get an answer of 48*pi*(a^4). Not sure if this seems right, as there is a ^4 value to a..?I am a bit confused here and want to make sure...

Hi, Thanks for both your replies. I tried working out the z limits again and get:( 4*(a^2)- (r^2)) and the second limit, I am guessing should be negative, if it has to cover the entire volume. The limits for r are a and 2a and for theta 0 and 2 pi. Is this right? Please help as I think I...

Hi, Thanks for your response, however I do not understand when you say "above the z=0 plane." Is my visualization of the diagram correct? In the sense its a cylinder in a sphere right?

Homework Statement Let D be the region x^2 + y^2 + z^2 <=4a^2, x^2 + y^2 >= a^2, and S its boundary (with outward orientation) which consists of the cylindrical part S1 and the spherical part S2. Evaluate the ux of F = (x + yz) i + (y - xz) j + (z -((e^x) sin y)) k through (a) the whole...