Question

SET the following two integrals. Do not calculate.

17a. Find the volume of the solid that lies within both cylinder ? ^2 + ?^ 2 = 1 and the sphere ?^ 2 + ?^ 2 + ?^ 2 = 4.

17b. Find the volume of the part of the ball ? ≤ ? that lies between the cones ? = ? 6 and ? = ? 3 .

Calculus 3 question. Please help.

Answer #1

sir given setup only. If any mistake plz comment.

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.

How to set up intergration of this problem --finding the volume
of the sphere x^2 + y^2 +z^2 ≤ 1 that lies in the 1st OCTANT,
x>0, y>0, and z>0. Give example of using double
integral setup --- IF POSSIBLE -- show set up using 3
integration.
Please explain how to set up integrals in CARTESIAN
coordinates.

Set up (Do Not Evaluate) a triple integral that yields the
volume of the solid that is below
the sphere x^2+y^2+z^2=8
and above the cone z^2=1/3(x^2+y^2)
a) Rectangular coordinates
b) Cylindrical
coordinates
c) Spherical
coordinates

find the volume of the solid below the surface z=2-square root (
1+x2+y2)and above the xy-plane
can someone help with this I am in calculus 3 ( multivariable
calculus)?

Set up the integral (do not evaluate) to find the volume of the
solid generated by revolving the region about the line x=5.
The region is bounded the graphs x=y^2, x=4
Use the disk and shell methods.

#6) a) Set up an integral for the volume of the solid S
generated by rotating the region R bounded by x= 4y and y= x^1/3
about the line y= 2. Include a sketch of the region R. (Do
not evaluate the integral).
b) Find the volume of the solid generated when the plane region
R, bounded by y^2= x and x= 2y, is rotated about the
x-axis. Sketch the region and a typical shell.
c) Find the length of...

find the volume of the following solid . The solid common two
the two cylinders x^2 +y^2=49 and x^2+z^2=49 the volume is.?
please list all steps even the most trivial. Thank you

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

A>Set up an integral that calculates the volume of the solid
described below using the washer method. Do not
evaluate the integral. f(x) = (x − 1)^2 − 1, x = −1, x = 1, y = 3,
about x = −3
B>Set up another integral that calculates the volume of the
solid from A using the shell method. Again, do not
evaluate the integral.
Include sketches for the following A AND B
Please write down the detailed process, thank...

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