Question

1. Suppose you have a circular tank with a 3 meter diameter and 2 meter height that is completely filled with water. Set up, DO NOT EVALUATE, a single integral to find the work required to empty the entire tank. Note that water weighs 9800 kg/m3 .

2.Consider the region bounded by the curves y =x^2 and y = 3x is rotated about the x-axis. Use the disc/washer method to set up, DO NOT EVALUATE, a single integral to find the volume of the resulting solid.

Answer #1

1) Set up, but do not evaluate, an integral to find the volume
when the region bounded by y=1, y=tanx and the y-axis is rotated
about the following lines:
a) The x-axis
b) The y-axis
c) The line y=2
d) The line x=3
e) The line x= -1
2) Set up, but do not evaluate, an integral to find each of the
following:
a) The volume that results when the region in the first quadrant
bounded by y=sinx, y=1 and...

Consider the region bounded by ? = 4? , ? = 1 and x-axis. Set
up the appropriate integrals
for finding the volumes of revolution using the specified
method and rotating about the specified axis. Be sure to first
sketch the region and draw a typical cross section. SET UP THE
INTEGRALS ONLY. DO NOT evaluate the integral.
a) Disc/washer method about the x-axis
b) Shell method about the y-axis
c) Disc/washer method about the line ? = 2.
d)...

The region is bounded by y=2−x^2 and y=x. (a) Sketch the region.
(b) Find the area of the region. (c) Use the method of cylindrical
shells to set up, but do not evaluate, an integral for the volume
of the solid obtained by rotating the region about the line x = −3.
(d) Use the disk or washer method to set up, but do not evaluate,
an integral for the volume of the solid obtained by rotating the
region about...

Set up, but do not evaluate, an integral to find each of the
following:
a) The volume that results when the region in the first quadrant
bounded by y=sinx, y=1 and the y-axis is rotated about the
x-axis.
b) The volume that results when the region that is bounded by
y=x3 , y=8 and the y-axis is rotated about the y-axis. c) The
volume when the region bounded by y=ex , x=1, the x-axis and the
y-axis is rotated about...

Suppose you have a cylindrical water tank with a height of S
meters with a height of 8 meters and a radius of 2 meters and that
it stands upright on its circular base and is half-full of water.
Determine the work required to empty the tank by pumping the water
to a level of 2 meters above the top of the tank.

1. The region bounded by y=x8 and y=sin(πx/2) is
rotated about the line x=−7.
Using cylindrical shells, set up an integral for the volume of the
resulting solid.
2.The region bounded by y=9/(1+x2), y=0, x=0 and x=8
is rotated about the line x=8.
Using cylindrical shells, set up an integral for the volume of the
resulting solid.

a.) Let S be the solid obtained by rotating the region bounded
by the curves y=x(x−1)^2 and y=0 about the y-axis. If you sketch
the given region, you'll see that it can be awkward to find the
volume V of S by slicing (the disk/washer method). Use cylindrical
shells to find V
b.) Consider the curve defined by the equation xy=12. Set up an
integral to find the length of curve from x=a to x=b. Enter the
integrand below

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.

Let R be the region of the plane bounded by y=lnx and the x-axis
from x=1 to x= e. Draw picture for each
a) Set up, but do not evaluate or simplify, the definite
integral(s) that computes the volume of the solid obtained by
rotating the region R about they-axis using the disk/washer
method.
b) Set up, but do not evaluate or simplify, the definite
integral(s) that computes the volume of the solid obtained by
rotating the region R about...

(Integration Application) A water tank is shaped like an
inverted cone with a height 2 meters and top radius 6 meters is
full of water. Set up a Riemann Sum and an Integral to model the
work that is required to pump the water to the level of the top of
the tank? No need to integrate here. (Note that density of water is
1000 kg/m3 ).
RIEMANN SUM ______________________________________________
INTEGRAL____________________________________________________
Provide an explanation as to the difference of the...

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