Question

Find 6 different iterated triple integrals for the volume of the tetrahedron cut from the first octant (when x > 0, y > 0, and z > 0) by the plane 6x + 2y + 3z = 6. Dont evaluate the integrals.

Answer #1

I have solved the first iterated of volume integral and you need not to do solved it.

Find the volume of the solid using triple integrals. The solid
region Q cut from the sphere x^2+y^2+z^2=4 by the cylinder r=2sinϑ.
Find and sketch the solid and the region of integration R. Setup
the triple integral in Cartesian coordinates. Setup the triple
integral in Spherical coordinates. Setup the triple integral in
Cylindrical coordinates. Evaluate the iterated integral

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.

6. Let R be the tetrahedron in the first octant bounded by the
coordinate planes and the plane passing through (1, 0, 0), (0, 1,
0), and (0, 0, 2) with equation 2x + 2y + z = 2, as shown below.
Using rectangular coordinates, set up the triple integral to find
the volume of R in each of the two following variable orders, but
DO NOT EVALUATE.
(a) triple integral 1 dxdydz
(b) triple integral of 1 dzdydx

1- Set up the triple integral for the volume of the sphere Q=8
in rectangular coordinates.
2- Find the volume of the indicated region.
the solid cut from the first octant by the surface z= 64 - x^2
-y
3- Write an iterated triple integral in the order dz dy dx for
the volume of the region in the first octant enclosed by the
cylinder x^2+y^2=16 and the plane z=10

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 a triple integral to find the volume of the given solid.
The tetrahedron enclosed by the coordinate planes and the
plane
11x + y + z = 2

Use a doubleintegral to find the volume of the
tetrahedron with vertices (0,0,0), (2,0,0), (0,4,0),
(0,0,12)
Make sketch. Set up, but do not evaluate, six
different iterated integrals that give the volume of the
tetrahedron.

USING ITERATED INTEGRALS, find the area bounded by the
circle x^2 + y^2 = 25,
a.) the x-axis and the parabola x^2 − 2x = y
b.) y-axis and the parabola y = 6x − x^2
b.) (first quadrant area) the y-axis and the parabola x^2 − 2x =
y

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

Use Lagrange multipliers to find the volume of the largest
rectangular box in the first octant with three faces in the
coordinate planes and one vertex in the given plane.
x + 4y + 3z = 12

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 23 minutes ago

asked 26 minutes ago

asked 32 minutes ago

asked 37 minutes ago

asked 40 minutes ago

asked 52 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago