Question

Let R be the region bounded by y = x^{2} + 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.**

Answer #1

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.

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 = 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.

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.

A. For the region bounded by y = 4 − x2 and the x-axis, find
the volume of solid of revolution when the area is revolved
about:
(I) the x-axis,
(ii) the y-axis,
(iii) the line y = 4,
(iv) the line 3x + 2y − 10 = 0.
Use Second Theorem of Pappus.
B. Locate the centroid of the area of the region bounded by y
= 4 − x2 and the x-axis.

Let X be the region bounded by y=x and y=x^2.
Find the volume of the solid that is made when X is revolved
about the y-axis. Find it in two different methods, include a
diagram for each method, and explain.

Let R be the region in enclosed by y=1/x, y=2, and x=3. a)
Compute the volume of the solid by rotating R about the x-axis. Use
disk/washer method. b) Give the definite integral to compute the
area of the solid by rotating R about the y-axis. Use shell
method. Do not evaluate the integral.

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...

Consider the region bounded by y=sqrt(x) and y=x^3
a) Find the area of this region
b) Find the volume of the solid generated by rotating this
region about the x-axis using washer
c) Find the volume of the solid generated by rotating this
region about the horizontal line y=3 using shells

Let B be the region bounded by the part of the curve y = sin x,
0 ≤ x ≤ π, and the x-axis. Express (do not evaluate) the volume of
the solid obtained by rotating the region B about the y-axis as
definite integrals
a) using the cylindrical shell method
b) using the disk method

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 7 minutes ago

asked 12 minutes ago

asked 20 minutes ago

asked 27 minutes ago

asked 34 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