(1 point) The region in the first quadrant bounded by y=4x2 ,
2x+y=6, and the y-axis...
(1 point) The region in the first quadrant bounded by y=4x2 ,
2x+y=6, and the y-axis is rotated about the line x=−2. The volume
of the resulting solid is: ____
Solutions
Expert Solution
we will use cyllinder / shell method to find volume
Consider a solid object with the base in the first quadrant
bounded by y(x) = 1-( x^2/16) , x-axis, and y-axis. If the cross
section that perpendicular to the x-axis is in the form of square,
determine the volume of this object!
Let R be the two-dimensional region in the first quadrant of the
xy- plane bounded by the lines y = x and y = 3x, and by the
hyperbolas xy = 1 and xy = 3. Let (x,y) = g(u,v) be the
two-dimensional transformation of the first quadrant defined by x =
u/v, y = v.
a) Compute the inverse transformation g−1.
b) Draw the region R in the xy-plane and the region g−1(R) in
the uv-plane
c) Use the...
9) R is the region bounded by the curves ? = x^3 , y=2x+4 , And
the y-axis.
a) Find the area of the region.
b) Set up the integral you would use to find the volume of a
solid that has R as the base and square cross sections
perpendicular to the x-axis.
Consider the region bounded between y = 3 + 2x - x^2 and y = e^x
+ 2 . Include a sketch of the region (labeling key points) and use
it to set up an integral that will give you the volume of the solid
of revolution that is obtained by revolving the shaded region
around the x-axis, using the... (a) Washer Method (b) Shell Method
(c) Choose the integral that would be simplest to integrate by hand
and integrate...
Sketch the region in the first quadrant enclosed by y=2/x ,
y=3x, and y=1/3x. Decide whether to integrate with respect to x or
y. Then find the area of the region.
Area =
Find the area of the region enclosed between y=4sin(x) and
y=2cos(x) from x=0 to x=0.4π
Hint: Notice that this region consists of two parts.
The region bounded by y=(1/2)x, y=0, x=2 is rotated around the
x-axis.
A) find the approximation of the volume given by the right
riemann sum with n=1 using the disk method. Sketch the cylinder
that gives approximation of the volume.
B) Fine dthe approximation of the volume by the midpoint riemann
sum with n=2 using disk method. sketch the two cylinders.