I just want to know how to set up the integral for this problem. Use spherical coordinates to find the volume of the solid in the first octant that lies inside a cone and a sphere.This is for practice to prepare for the real problem with functions.
this is what I think how it should look like V=[0,π/2]∫() [0,π/2]∫() [ρ1,ρ2]∫()dρdφdθ Do you think i set it up right?

  1. 👍 0
  2. 👎 0
  3. 👁 137
  1. Your volume element is a weird amalgam of rectangular and cylindrical coordinates.

    The volume element in spherical coordinates is
    dv = r^2 sinθ dρ dφ dθ
    In cylindrical coordinates,
    dv = ρ dρ dφ dz

    google can provide you with examples, such as

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Physics, Calculus(alot of stuff together)= HELP!!

    A rod extending between x=0 and x= 14.0cm has a uniform cross- sectional area A= 9.00cm^2. It is made from a continuously changing alloy of metals so that along it's length it's density changes steadily from 2.70g/cm^3 to

  2. Physics

    Four objects - a hoop, a solid cylinder, a solid sphere, and a thin, spherical shell - each has a mass of 4.59 kg and a radius of 0.252 m. (a) Find the moment of inertia for each object as it rotates about the axes shown in the

  3. Calculus

    online class and I don't know what to do so I posts. Any help is great.Thank you Convert the integral [0,1]∫ [0,√(1-x^2 -y^2)]∫𝑧√(x^2 +y^2 +z^2)dz dy dx into anequivalent integral in spherical coordinates and evaluate

  4. Calculus

    If f(x) and g(x) are continuous on [a, b], which one of the following statements is true? ~the integral from a to b of the difference of f of x and g of x, dx equals the integral from a to b of f of x, dx minus the integral from a

  1. math

    Note: You can get full credit for this problem by just answering the last question correctly. The initial questions are meant as hints towards the final answer and also allow you the opportunity to get partial credit. Consider the

  2. Calculus

    The region enclosed by the graph of y = x^2 , the line x = 2, and the x-axis is revolved abut the y-axis. The volume of the solid generated is: A. 8pi B. 32pi/5 C. 16pi/3 D. 4pi 5. 8pi/3 I solved for x as √y and set up this

  3. Math (Definite Integrals)

    Sketch the region given by the definite integral. Use geometric shapes and formulas to evaluate the integral (a > 0, r > 0). r ∫ sqrt(r^2 - x^2) dx -r While I recognize that this looks similar to a circle function, I'm not sure

  4. Calculus I

    A spherical balloon is inflated at a rate of 10 cm^3/min. How fast does the radius change when the radius is 20 cm? Need help with set up and work through of problem.

  1. Calculus 3: Spherical Coordinates

    Use spherical coordinates to calculate the triple integral of f(x, y, z)=y over the region x^2+y^2+z^2≤8, x, y, z ≤ 0.

  2. calc II

    Express the integrals as the sum of partial fractions and evaluate the integral: (integral of) (x^2)dx/(x-1)(x^2 +2x+1) My work: The above integral is equal to x^2dx/(x+1)^2 (A/x-1) + (B/x+1) + (Cx+D)/(x+1)^2 = x^2 A(x+1)^2 +

  3. integral confusion

    integral of Sec[2x]Tan[2x] i know u is sec 2x du=2sec2xtan2x dx what would i have to multiply with du so it would equal tan 2x dx? if my question is confusing, then here's another example of what i'm talking about: integral of

  4. math

    use spherical coordinates to evaluate the triple integral of (e^-(x^2+y^2+z^2))/(sqrt(x^2+y^2+z^2)dV where E is the region bounded by the spheres x^2+y^2+z^2=49 and x^2+y^2+z^2=81???

You can view more similar questions or ask a new question.