Question

Let R be the region bounded by 6 cos x, y = e^x , x = 0, and ? =pi /2 . Using a method of your choice, find the volume of the solid generated by revolving R around the line y = 7. Give an exact numerical answer.

Answer #1

Let R be the region bounded by y=ln(x), the x-axis, and
the line x=e. Find the volume of the solid that is generated when
the region R is revolved about the x-axis.

Let R be the region bounded by y = x2 + 1, y = 0, x =
1, and x = 2. Graph the region R. Find the
volume of the solid generated when R is revolved
about the y-axis using (a) the Washer Method and
(b) the Shell Method.

Consider the region R bounded by y = sinx, y = −sinx , from x =
0, to x=π/2.
(1) Set up the integral for the volume of the solid obtained by
revolving the region R around
x = −π/2
(a) Using the disk/washer method.
(b) Using the shell method.
(2) Find the volume by evaluating one of these integrals.

Let R in the x,y-plane be in the first quadrant and bounded by
y=x+2 and y=x2, and x = 0. Find the
volume generated by revolving the region R about the line x =
4.

The region R is bounded by y=x^2 and y=sqrtx. Find the volume of
the solid generated by revolving R about
a) the x-axis b) the y-axis c) the line y=1 d) the line y=-1 e)
the line x=1 f) the line x=-1

Let R be the region bounded by y = ln(x), the x-axis, and the
line x = π.
a.Usethecylindrical shell method to write a deﬁnite integral
(BUTDONOTEVALUATEIT) that gives the volume of the solid obtained by
rotating R around y-axis
b. Use the disk (washer) method to write a deﬁnite integral (BUT
DO NOT EVALUATE IT) that gives the volume of the solid obtained by
rotating R around x-axis.

R is the region bounded by ? = √? − 1, ? = 2, and the
x-axis.
a) Set up the integral you would use to find the volume of the
solid formed by revolving R around the y-axis.
b) Set up the integral you would use to find the volume of the
solid formed by revolving R around the line ? = −3
c) Set up the integral you would use to find the volume of the
solid formed...

Let R be the region bounded by the curves y = x, y = x+ 2, x =
0, and x = 4. Find the volume of the solid generated when R is
revolved about the x-axis. In addition, include a carefully labeled
sketch as well as a typical approximating disk/washer.

Find the volume of the solid generated by revolving the region
bounded by the graphs of y = e x/4 , y = 0, x = 0, and x = 6 about
the x−axis.
Find the volume of the solid generated by revolving the region
bounded by the graphs of y = √ 2x − 5, y = 0, and x = 4 about the
y−axis.

Using the Shells method, find the volume of the solid generated
by revolving the region bounded by
y = 5 - x, y = 0, x = 0
about the line y = -1.

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