1. J

    Moment of Inertia of a Solid Cone

    How to find the moment of inertia about the z axis of the top half of a solid cone using Spherical Coordinates? This what I did! I = ∫ R^2 dm where I is the moment of inertia and R is the perpendicular distance from the axis of rotation to the slant height of the cone changing dm with...
  2. T

    Triple Integrals; Volume of Solids within Boundaries

    Hello, everyone. So here is the problem in question with their respective answers: Let W1W1 be the solid half-cone bounded by z=x2+y2−−−−−−√z=x2+y2, z=3z=3 and the yzyz-plane with x≥0x≥0, and let Let W2W2 be the solid half-cone bounded by z=x2+y2−−−−−−√z=x2+y2, z=5z=5 and the xzxz-plane with...
  3. X

    triple integral

    i was told that the ſ ſ ſ dzdxdy = volume , however , if i have ſ ſ ſ z(dzdxdy) , is it still volume ?
  4. X

    triple integral in polar coordinate

    why x is p(cosθ)(sinφ) ? and y=p(sinθ)(cosφ)? z=p(cosφ) As we can see, φ is not the angle between p and z .......
  5. X

    limit of triple integrals

    how to get the limit of theta in this question ? in this question , the author found that the linit of theta is from 0 to pi/2 what i did is : since we know that , x= r cos theta , so 1 = 1 cos theta , so , theta = 2pi is the working correct ?
  6. X

    calculating volume using double or triple integral

    which is correct ? i have 2 notes below . Which way is correct ?
  7. M

    Volume triple integrals

    I need to calculate the volume formed by z=1 and x^2+y^2=8z. Y used cylindrical coordinated and I got r^2=8z and z=1. Is this OK? r from 0 to Sqrt 8 Theta from 0 to 2Pi z from r^2/8 to 1 Thanks
  8. M

    Triple integral volume

    I need to calculate the volume formed by the cone x2+y2=3z2 and the cylinder x2+y2=4y. I drew both figures and with cylindrical coordinates I got this triple integral: I don't know if I got the right triple integral. Assuming the triple integral is right, the answer I got is 128π/(3√3). I...
  9. B

    Check these two Triple Integrals (cylindrical and spherical)

    Sphere Work (the picture I drew is an xy trace of the sphere, if that isn't clear) The sphere problem asks you to find the volume of the region bounded by the plane z=1/2 and a ball with radius 1 centered at the origin using spherical coordinates. I'm not even...
  10. Jason76

    Triple Integral

    How would the first step be accomplished, changing the limits of integration of the most inner limits of integration? \sqrt{200 - x^{2} - y^{2} and x^{2} + y^{2} I understand that a conversion formula is needed, but the Cartesian coordinates given are not single numbers, but are square roots.
  11. alexmahone

    Primitive Pythagorean triple

    Prove that for any primitive Pythagorean triple (a, b, c), exactly one of a and b must be a multiple of 3, and c cannot be a multiple of 3. My attempt: Let a and b be relatively prime positive integers. If $a\equiv \pm1 \pmod{3}$ and $b\equiv \pm1 \pmod{3}$, $c^2=a^2+b^2\equiv 1+1\equiv 2...
  12. B

    Set up triple integrals in Cylindrical and Spherical coordinates

    I have no idea to set this integral, please help: 1, the first octane bounded above by z=x and x2+y2 = 4 for triple integral in Cylindrical coordinate: This is what i have (1st integral) 0 to pi/2 (2nd integral) 0 to 1 (3rd integral) rcos(theta) to (1-r2) then r dz dr dtheta 2, Triple...
  13. H

    Triple Integral

    Hello Can you help to solve this triple integral wich is in the attachment as well Intg ntg intg z*(x^2+y^2)^(1/2) dxdydz over the area A which is (x,y,z): x^2+(y-1)^2 >= 1 and 0<=z>=2 By using cylindrical coordinates Thanks
  14. A

    order of integration, triple integral

    Hi I am struggling to get going on the following problem: V is the region bounded by surfaces x=0 and x=9-y^2 -9z^2 express the integral int int int f(x,y,z)dV as an iterated integral in two orders: (i) dx dy dz and (ii) dy dx dz I am having trouble trying to figure out the region V so I can...
  15. S

    Solving triple integral by switching to cylindrical coordinates

    Hello, everyone. This is me posting for the first time here, so have mercy (haha). Recently I have come across an integral that's been bugging me ever since. The problem is to calculate the integral where the region D represents the intersection of two...
  16. A

    Find the value of k from a triple equation system

    Hello, I would like to get some help to solve a problem I have to do for my Math course. Any help will be much appreciated. Here how it goes... I have to find all values of "k", for which one the system will have a not null solution. Here is the system: kx + 5y + kz = 0 x - ky - z = 0 2x -...
  17. J

    Vector Calc- Maximizing the Domain of a triple integral

    What domain D in space maximizes the value of the integral . Justify your answer and find the maximum value of the integral.
  18. F

    Evaluating triple integral - undefined point?

    I'm looking at the following triple integral: When evaluating the part from 0 to 2pi for...
  19. J

    Improper triple integral - Vector Calc

    I tried changing this into spherical coordinates, but I ended up with the p3/2sin(phi)/(cos(phi)+p2(1/2) which I can't figure out. I'm not sure if I did something wrong when switching coordinate systems, or if there's just an alternate way to solve, but I'm stuck. Any suggestions would be really...
  20. D

    Triple loan

    A Bank approves 3 loans for a customer: L#1, L#2 and L#3. L#1: 2 years (24 months), rate of 12% annual cpd. monthly. L#2: 3 years (36 months), rate of 9% annual cpd. monthly. L#3: 4 years (48 months), rate of 6% annual cpd. monthly. Amount borrowed of L#2 is twice that of L#1...