Copyright

Evaluate triple integral 2(x^3 + xy^2) dV, where E is the solid in the first octant that lies...

Question:

(a) Evaluate {eq}\iiint (2x^{3}+xy^{2})dV , {/eq} where {eq}E {/eq} is the solid in the first octant that lies beneath the paraboloid {eq}z=4-x^{2}-y^{2} {/eq}

b) Evaluate the integral, where E is enclosed by the paraboloid {eq}z=5+x^{2}+y^{2} , {/eq}, the cylinder {eq}x^{2}+y^{2}=6 {/eq} and the xy-plane {eq}\iiint e^{z}dV {/eq}

Multiple Integral:

The multiple integral is the type of integral which contains more then one variable. The given multiple integral can be evaluated by using the cylindrical coordinates:

{eq}\displaystyle \iiint_E f(x, y, z) \, dV = \iiint_R f(r, \, \theta, \, z)\cdot r \,\, dz\,dr\,d\theta {/eq}.

Answer and Explanation: 1

Become a Study.com member to unlock this answer!

View this answer

(a)

The given integral is:

{eq}\displaystyle \iiint_E 2x^{3} + xy^{2} \, dV {/eq}

Where,

E lies beneath the paraboloid {eq}z = 4 - x^{2} -...

See full answer below.


Learn more about this topic:

Loading...
Cylindrical & Spherical Coordinates: Definition, Equations & Examples

from

Chapter 13 / Lesson 10
23K

Learn how to convert between Cartesian, cylindrical and spherical coordinates. Discover the utility of representing points in cylindrical and spherical coordinates.


Related to this Question

Explore our homework questions and answers library