1. L

    Pythagorean triple integers' occurrence

    Is there a limit to how many times a particular integer may appear in different Pythagorean triples?
  2. S

    Calculating Volume using Triple Integral

    **I am trying to solve this problem but I am having difficulties to finish it. I would appreciate of someone can advice me on how to continue** **Problem:** Calculate $$\iiint_{V} Z\mathrm dV$$ where E is defined by $$ x^2+y^2 \le z^2 $$and$$ x^2+y^2=z^2 \le R^2 with R\gt0$$ **Solution** Using...
  3. S

    Volume with Triple Integral

    I have attached here solution to a problem. Please I wish to find out if my approach is correct
  4. S

    triple Integral

    I wish to find out if my approach to this question is correct
  5. S

    triple Integral

    I have solved the attached question. I wish to find out if my approach is correct
  6. Z

    Triple Integral of a complex geometric shape

    Boundaries: z = 0 z = x + 2y z = 4 - x - 3y z = -y Answer: \int_{0}^{4} \int_{-z}^{4-2z} \int_{z-2y}^{4-z-3y} ~dx~dy~dz = \frac {32}{3} I would be much appreciated if anyone show me the steps of setting the above boundaries...
  7. Z

    Triple integral density of a strange shape.

    x = 0 y = 0 z = 0 x + y = 1 z = x + 2y Density(x, y, z) = 3 + 2x + 2y - 2z Answer: 1/6 My Solution (not correct) \int_{0}^{1} \int_{0}^{1-x} \int_{0}^{x+2y} (3+2x+2y-2z) ~dz~dy~dx = 5/3 What did I do wrong?
  8. Z

    Triple Integral Exercise!

    Evaluate \int_{0}^{1} \int_{0}^{x} \int_{0}^{ \sqrt{x^2+y^2} } (x^2+y^2)^{3/2} / ( x^2 + y^2 + z^2 ) ~dz~dy~dx Answer: { \pi } / { 12 } 1. What would be the best coordinate system to solve this problem? 2. Would anyone show me how to solve this problem with spherical coordinate?
  9. SenatorArmstrong

    Graphing a triple integral

    Hello forum! I am trying to graph this triple integral. $$\int\limits_{-1}^{1}\int\limits_{y}^{(y+3)}\int\limits_{(x+2)}^{(x+4)} f(x,y,z) \,dz\,dx\,dy$$ I would present my attempt, but it simply looks like a 3D coordinate systems with a bunch of lines drawn in places that I believe...
  10. SenatorArmstrong

    Triple integral question

    Hello folks. I have a question on this triple integral. $$\iiint_S z \,dx\,dy\,dz$$ where S is bounded by $x+y+z=2$, $x=0$, $y=0$, and $z=0$ I have the work on my white board. I got an answer of $\frac{5}{4}$ ... I sketched out a 3D coordinate system and noticed that this looks like a...
  11. I

    Triple Integral with Spherical Coordinates

    Calculate the Integral bellow, where T is the region inside the cylinder x² + y² = 1 and x² + y² + z² = 4. ∫ ∫ ∫ (x² + y²)dV T I'm having trouble to convert the coordinates... I did it like this (feel free to correct me, after all, probrably I'm wrong) 0 < x <sqrt(1 - y²) -1...
  12. I

    Triple Integral with Spherical Coordinates

    See my post here.
  13. T

    Dice question, roll a double triple twice in a row

    New question... 6 dice. What are the odds of rolling a douple triple twice in a row? Example: First roll is 2-2-2-3-3-3. Next roll is also a double triple; say 1-1-1-6-6-6. Thanks, Matt
  14. S

    Triple integral

    x^2+y^2=z 0<z<4 if I substitute z in the first equation I get x^2+y^2=4. So my bounds would be: 0<phi<2pi 0<r<2 and now I'm not sure whether z will be from 0 to 4 or 0 to r^2?
  15. L

    All prime Pythagorean triple

    Does there exist a Pythagorean triple consisting only of prime numbers?
  16. S

    Triple integrals

    I tried solving these like 100 times but every time I get answer different from the one in the book. I'm not sure whether I make mistake or they just wrote a wrong answer. I would be thankful if someone can check them for me :) If you can't read from the pics: 1. 1≤x^2+y^2+z^2≤4 I...
  17. Z

    Solving cylinder with spherical coordinate triple integration

    Consider the region R within the cylinder x^2 + y^2 <= 4, bounded below by z = 0 and above by z = 2 - y. Assume a mass density = z. Set up and evaluate the integral representing the mass of the solid. This is easy with cylinderical coordinates: \int_{0}^{ 2\pi} \int_{0}^{2}...
  18. I

    Triple integral over a tetrahedron

    Hi, Can someone help me to compute the volume of the tetrahedron by triple integral? (see figure attached). I need help please... Let's suppose, for example, we have integrand f(xi,eta,zeta)=1, and I want to compute the volume by triple integral, how should the limits be defined...
  19. S

    Triple integral

    Okay so I have given the following problem and the solutions says that the angle phi is between -pi/2 and pi/2 and I'm not sure how do we get that? I'm asked to find the mass.
  20. Z

    Requesting help for this simple triple integral..

    The region is bounded by x^2+y^2=3, z=-1, z=2 \int_{}^{} \int_{}^{} \int_{}^{} y dxdydz I managed to setup the following boundary, but it yielded zero \int_{-1}^{2} \int_{-sqrt(3)}^{sqrt(3)} \int_{-sqrt(3-y^2)}^{sqrt(3-y^2)} y dxdydz so.. I reshape the boundaries to avoid...