Find the volume V of the described solid S. The base of S is the
triangular...
Find the volume V of the described solid S. The base of S is the
triangular region with vertices (0, 0), (2, 0), and (0, 2).
Cross-sections perpendicular to the x−axis are squares.
Find the volume for the solid, whose base is between the curves
y=2x and y=x^2 over [0,2] and whose cross sectional slices are
squares perpendicular to the x-axis and perpendicular to the base.
Include a sketch of your base and show the slice orientation.
Consider the solid S with the following properties: • The base
of S is the triangle T with vertices (0, 0),(1, 0), and (0, 1). •
When S is sliced perpendicularly to the x-axis, it has square cross
sections.
(a) (4 points) Sketch the base T and determine the equations of
its three edges.
(b) (3 points) Set up an integral to compute the volume of
S.
(c) (3 points) Evaluate the integral from part (b).
A volume is described as follows:
1. the base is the region bounded by x = − y 2 + 16 y + 5 and x
= y 2 − 30 y + 245 ;
2. every cross section perpendicular to the y-axis is a
semi-circle. Find the volume of this object.
Find the volume of the solid by subtracting two volumes, the
solid enclosed by the parabolic cylinders
y = 1 − x2, y = x2 − 1 and the planes x +
y + z = 2, 5x + 2y − z + 13 = 0.
Find the volume of the solid by subtracting two volumes, the
solid enclosed by the parabolic cylinders y = 1 − x2, y = x2 − 1
and the planes x + y + z = 2, 3x + 3y − z + 15 = 0.
Find the volume of the solid using triple integrals. The solid
bounded below by the cone
z= sqr
x2+y2 and bounded above by the sphere
x2+y2+z2=8.(Figure)
Find and sketch 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 triple integral in Cylindrical coordinates.
Consider N massless non-interacting spin-s fermions in a
three-dimensional box of volume V .
(a) Find the Fermi energy EF as a function of N, V , and
s.
(b) For zero temperature, find the pressure in terms of N, V , and
EF .
(c) Plot the occupation of states as a function of the energy at a
temperature of T =EF /(10k). Your graph can be a sketch
by hand. However, the effect of the finite temperature should...
4) Find the volume of the solid formed by the region bounded by
the graphs of y= x3 , y=x for x=0 and x=1
-Sketch the region bounded by the graphs of the functions and
find the area of the region bounded by the graphs of y=x-1 and y=
(x − 1)3
-calculate the arc length of the graph y= x=1 to x=2 14x7 +
101x5 from
-Use the washer method to find the volume of the solid formed by...