Question

1. Answer Following Questions, Show work, clear hand writing, thank you

a. Set up (i.e. DO NOT SOLVE) an integral to find the volume of the solid obtained when the given region is rotated about the given axis. The region bounded by y = 2x^2 and y = 2x^3 about the line x = −1

b. get the general antiderivative of f(x) = (x^2)*(e^−x)

c. Find the length of the polar curve r = 2cosθ

Answer #1

#6) a) Set up an integral for the volume of the solid S
generated by rotating the region R bounded by x= 4y and y= x^1/3
about the line y= 2. Include a sketch of the region R. (Do
not evaluate the integral).
b) Find the volume of the solid generated when the plane region
R, bounded by y^2= x and x= 2y, is rotated about the
x-axis. Sketch the region and a typical shell.
c) Find the length of...

Set up, but do not evaluate, an integral to find each of the
following:
a) The volume that results when the region in the first quadrant
bounded by y=sinx, y=1 and the y-axis is rotated about the
x-axis.
b) The volume that results when the region that is bounded by
y=x3 , y=8 and the y-axis is rotated about the y-axis. c) The
volume when the region bounded by y=ex , x=1, the x-axis and the
y-axis is rotated about...

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) Set up, but do not evaluate, an integral to find the volume
when the region bounded by y=1, y=tanx and the y-axis is rotated
about the following lines:
a) The x-axis
b) The y-axis
c) The line y=2
d) The line x=3
e) The line x= -1
2) Set up, but do not evaluate, an integral to find each of the
following:
a) The volume that results when the region in the first quadrant
bounded by y=sinx, y=1 and...

Question3: ( You just need to provide the final answer)
a）Calculate the area of the region enclosed by y = cos(x) and y
= sin(x) between x = 0 and x = π/4 .
b) Find the volume of the solid obtained when the the region
bounded by y = √x and y = x^3 is rotated around the x-axis.
c) Find the volume of the solid obtained when the the region
bounded by y = x^2 and y =...

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)...

2. Set up an integral to find the volume of the solid generated
when the region bounded by y = 2x2 and y = x3
is
(a) Rotated about the x-axis using shells
(b) Rotated about the x-axis using washers
(c) Rotated about the y-axis using shells
(d) Rotated about the y-axis using washers
(e) Rotated about the line x = −3
(f) Rotated about the line y = −2
(g) Rotated about the line y = 11
(h) Rotated...

Set up an integral to ﬁnd the volume of the solid generated when
the region bounded by y = square root(x) and y = (1/2)x is
(a) Rotated about the x-axis using washers
(b) Rotated about the line x = −4 using washers
(c) Rotated about the line y = 5 using shells

Set up the integral. you do NOT have to
integrate.
A region is bounded by the x-axis and y = sinx with 0 ≤
x ≤ π. A solid of revolution is obtained by rotating that region
about the line y =−2.

Using any method, SET UP, but do NOT evaluate, an integral
representing the volume of the solid obtained by rotating the
region bounded by the curves y = 1 x , y = 0, x = 1, x = 3 about
(a) the line y = −1 (b) the y-axis.

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