Question

The average value of a function f(x, y, z) over a solid region E is defined...

The average value of a function f(x, y, z) over a solid region E is defined to be fave = 1 V(E) E f(x, y, z) dV where V(E) is the volume of E. For instance, if ρ is a density function, then ρave is the average density of E. Find the average value of the function f(x, y, z) = 5x2z + 5y2z over the region enclosed by the paraboloid z = 4 − x2 − y2 and the plane z = 0.

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
1. Evaluate ???(triple integral) E x + y dV where E is the solid in the...
1. Evaluate ???(triple integral) E x + y dV where E is the solid in the first octant that lies under the paraboloid z−1+x2+y2 =0. 2.Evaluate ???(triple integral) square root ?x^2+y^2+z^2 dV where E lies above the cone z = square root x^2+y^2 and between the spheres x^2+y^2+z^2=1 and x^2+y^2+z^2=9
B is the solid occupying the region of the space in the first octant and bounded...
B is the solid occupying the region of the space in the first octant and bounded by the paraboloid z = x2 + y2- 1 and the planes z = 0, z = 1, x = 0 and y = 0. The density of B is proportional to the distance at the plane of (x, y). Determine the coordinates of the mass centre of solid B.
Use cylindrical coordinates. Evaluate the integral, where E is enclosed by the paraboloid z = 8...
Use cylindrical coordinates. Evaluate the integral, where E is enclosed by the paraboloid z = 8 + x2 + y2, the cylinder x2 + y2 = 8, and the xy-plane.    ez dV E
Use cylindrical coordinates. Evaluate the integral, where E is enclosed by the paraboloid z = 7...
Use cylindrical coordinates. Evaluate the integral, where E is enclosed by the paraboloid z = 7 + x2 + y2, the cylinder x2 + y2 = 8, and the xy-plane. ez dV E
Find the position of the center of mass of the solid defined by the region inside...
Find the position of the center of mass of the solid defined by the region inside the sphere x^2 + y^2 + z^2 = 2 and above the paraboloid z = x^2 + y^2 . The density is ρ (x, y, z) = z [kg / m3 ].
Find the integral that represents: The volume of the solid under the cone z = sqrt(x^2...
Find the integral that represents: The volume of the solid under the cone z = sqrt(x^2 + y^2) and over the ring 4 ≤ x^2 + y^2 ≤ 25 The volume of the solid under the plane 6x + 4y + z = 12 and on the disk with boundary x2 + y2 = y. The area of ​​the smallest region, enclosed by the spiral rθ = 1, the circles r = 1 and r = 3 & the polar...
Set up the triple integral, including limits, of the function over the region. f(x, y, z)...
Set up the triple integral, including limits, of the function over the region. f(x, y, z) = sin z, x ≥ 0, y ≥ 0, and below the plane 2x + 2y + z = 2
Let D be the solid region defined by D = {(x, y, z) ∈ R3; y^2...
Let D be the solid region defined by D = {(x, y, z) ∈ R3; y^2 + z^2 + x^2 <= 1}, and V be the vector field in R3 defined by: V(x, y, z) = (y^2z + 2z^2y)i + (x^3 − 5^z)j + (z^3 + z) k. 1. Find I = (Triple integral) (3z^2 + 1)dxdydz. 2. Calculate double integral V · ndS, where n is pointing outward the border surface of V .
Let E be the solid that lies between the cylinders x^2 + y^2 = 1 and...
Let E be the solid that lies between the cylinders x^2 + y^2 = 1 and x^2 + y^2 = 9, above the xy-plane, and below the plane z = y + 3. Evaluate the following triple integral. ?x2 +y2? dV
Integrate f(x,y,z) = z over the region enclosed by x^2+y^2=3^2 , z=x^2+y^2 and z=0.
Integrate f(x,y,z) = z over the region enclosed by x^2+y^2=3^2 , z=x^2+y^2 and z=0.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT