Question

The region is bounded by y = 2 − x^ 2 and y = x

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

Answer #1

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...

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...

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.

Consider the region in the xy-plane bounded by the curves y =
3√x, x = 4 and y = 0.
(a) Draw this region in the plane.
(b) Set up the integral which computes the volume of the solid
obtained by rotating this region about
the x-axis using the cross-section method.
(c) Set up the integral which computes the volume of the solid
obtained by rotating this region about
the y-axis using the shell method.
(d) Set up the integral...

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

Consider the plane region R bounded by the curve y = x − x 2 and
the x-axis. Set up, but do not evaluate, an integral to find the
volume of the solid generated by rotating R about 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.

Let S be the region between •x=1, •x=3, •y=6−(x−2)2, and •y=x
2+1.
a) Set up an integral to ﬁnd the area of S. Do not
evaluate.
b) Set up an integral to ﬁnd the volume Vx of the solid obtained by
rotating S about the x-axis. Do not evaluate.
c) Set up an integral to ﬁnd the volume Vy of the solid obtained by
rotating S about the y-axis. Do not evaluate.

Find the volume V of the solid obtained by rotating the
region bounded by the given curves about the specified line.
y = 5x4, y = 5x, x ≥
0; about the x-axis
Find the area of the region enclosed by the given curves.
y = 3 cos(πx), y = 12x2 −
3
Find the volume V of the solid obtained by rotating the
region bounded by the given curves about the specified line.
2x = y2, x = 0, y =
5; about the...

Please answer all question explain. thank you.
(1)Consider the region bounded by y= 5- x^2 and y = 1. (a)
Compute the volume of the solid obtained by rotating this region
about the x-axis.
(b) Set up the integral for the volume of the solid obtained by
rotating this region about the line x = −3. No need to evaluate the
integral, just set it up.
(2) (a) Find the exact (no calculator approximation) average
value of the function f(x)...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 6 minutes ago

asked 10 minutes ago

asked 10 minutes ago

asked 36 minutes ago

asked 38 minutes ago

asked 46 minutes ago

asked 53 minutes ago

asked 55 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago