Volume and Triple IntegralsWhen finding the volume of a solid using triple integrals, is the "integral" always ∫ ∫ ∫ dV, regardless of what the "z function" is?For instance, for the problem: Find the volume of the solid that lies within the sphere x 2 + y 2 + z 2 = 4, above the xy-plane, and below the cone z = x 2 + y 2 .Is the integral just ∫ ∫ ∫ dV with the correct bounds of integration, regardless of z = x 2 + y 2 ?

Question

Volume and Triple IntegralsWhen finding the volume of a solid using triple integrals, is the &quot;integral&quot; always   ∫  ∫  ∫ dV, regardless of what the &quot;z function&quot; is?For instance, for the problem: Find the volume of the solid that lies within the sphere       x    2    +      y    2    +      z    2    =  4, above the xy-plane, and below the cone   z  =             x      2        +          y      2      .Is the integral just   ∫  ∫  ∫ dV with the correct bounds of integration, regardless of   z  =             x      2        +          y      2      ?

falwsay · Accepted Answer

Explanation:If you have triple integral of type   ∭  F  D  V and region in some volume V. This means you are adding value of F over all points over V. But if F is 1, this means you&#039;re finding volume of V

Answered question

Answer & Explanation

New Questions in High school geometry