Question

Use a double integral in polar coordinates to find the volume of the solid bounded by the graphs of the equations.

z = xy^{2}, x^{2} + y^{2} =
25, x>0, y>0, z>0

Answer #1

please comments if you have any problem

use a double integral in polar coordinates to find the volume of
the solid in the first octant enclosed by the ellipsoid
9x^2+9y^2+4z^2=36 and the planes x=sqrt3 y, x=0, z=0

Use polar coordinates to find the volume of the given solid.
Under the paraboloid
z = x2 + y2
and above the disk
x2 + y2 ≤ 25

57.
a. Use polar coordinates to compute the (double integral (sub
R)?? x dA, R x2 + y2) where R is the region in the first quadrant
between the circles x2 + y2 = 1 and x2 + y2 = 2.
b. Set up but do not evaluate a double integral for the mass of
the lamina D={(x,y):1≤x≤3, 1≤y≤x3} with density function ρ(x, y) =
1 + x2 + y2.
c. Compute??? the (triple integral of ez/ydV), where E=
{(x,y,z):...

Use the triple integrals and spherical coordinates to find the
volume of the solid that is bounded by the graphs of the given
equations. x^2+y^2=4, y=x, y=sqrt(3)x, z=0, in first octant.

Use cylindrical coordinates to find the volume of the solid
bounded by the graphs of z = 68 − x^2 − y^2 and z = 4.

1a. Using rectangular coordinates, set up iterated integral that
shows the volume of the solid bounded by surfaces z= x^2+y^2+3,
z=0, and x^2+y^2=1
1b. Evaluate iterated integral in 1a by converting to polar
coordinates
1c. Use Lagrange multipliers to minimize f(x,y) = 3x+ y+ 10 with
constraint (x^2)y = 6

Find the integral that represents the volume of the solid
bounded by the planes y = 0, z = 0, y = x and 6x + 2y + 3z = 6
using double integrals.

Use polar coordinates to find the volume of the given solid.
Inside the sphere x2 + y2 + z2
= 16 and outside the cylinder x2 + y2 = 4

Set up a double integral in rectangular coordinates for the
volume bounded by the cylinders x^2+y^2=1 and y^2+z^x=1 and
evaluate that double integral to find the volume.

Write down a cylindrical coordinates integral that gives the
volume of the solid bounded above by z = 50 − x^2 − y^2 and below
by z = x^2 + y^2 . Evaluate the integral. (Hint: use the order of
integration dz dr dθ.)

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