Question

a.) Find the length of the curve y=ln(x),1 ≤ x ≤ sqrt(3)

b.) Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y^2=x and x=2y about the y-axis

c.) Find the volume of the solid that results when the region bounded by x=y^2 and x=y+12 is revolved about the y-axis

Answer #1

A. (1 point) Find the volume of the solid obtained by rotating
the region enclosed by ?= ?^(4?)+5, ?= 0, ?= 0, ?= 0.8
about the x-axis using the method of disks or washers. Volume =
___ ? ∫
B. (1 point) Find the volume of the solid obtained by rotating
the region enclosed by ?= 1/(?^4) , ?= 0, ?= 1, and ?= 6,
about the line ?= −5 using the method of disks or washers.
Volume = ___?...

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

Find the surface area of the solid generated when the
region bounded by x=ln(2y+1),0≤y≤1 is revolved about the Y-
axis.

(1 point) Find the volume of the solid obtained by rotating the
region enclosed by
y=e^4x+4,y=0,x=0,x=1
about the x-axis using the method of disks or washers.

Set up an integral to find the volume of solid obtained by
rotating about the given axis, the region bounded by the curves
y=2x and x= sqrt 2y. Sketchh!! Axis - Y axis (Washer and Shell)

1. Find the area of the region between the curves y = x - 1 and
y2 = 2x + 6 .
2. Find the volume of the solid of revolution formed by rotating
the region about the y-axis bounded by y2 = x and x =
2y.

1- Find the volume of the solid obtained by rotating the region
bounded by the given curves about the specified axis.
?= 64x− 8x^2, y=0;
about the y-axis
2- Find the volume of the solid obtained by rotating the region
bounded by the given curves about the specified axis.
y= 5+ 1/x^2, y= 5, x=2, x=9;
about the x-axis.

Problem (9). Let R be the region enclosed by y = 2x, the x-axis,
and x = 2. Draw the solid and set-up an integral (or a sum of
integrals) that computes the volume of the solid obtained by
rotating R about:
(a) the x-axis using disks/washers
(b) the x-axis using cylindrical shells
(c) the y-axis using disks/washer
(d) the y-axis using cylindrical shells
(e) the line x = 3 using disks/washers
(f) the line y = 4 using cylindrical...

Using the Method of Cylindrical Shells, find a definite integral
that gives the volume V of the solid S obtained by rotating the
region R bounded by curves: y=sqrt[x] ,and y=0 about the
x-axis.
There is a 3rd line at x=4

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...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 18 minutes ago

asked 39 minutes ago

asked 43 minutes ago

asked 48 minutes ago

asked 53 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

asked 1 hour ago