Question

Consider the region bounded by the line y = 2x and the parabola
y = 2x^{2}-2x.

a. Evaluate the volume obtained by rotating this region about the line x = -5

b. Evaluate the volume obtained by rotating this region about the line y = -10

Answer #1

consider the region r bounded by the parabola y=4x^2 and the
lines x=0 and y=16 find the volume of the solid obtained by
revolving R about the line x=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...

Consider the region bounded by y = sin x and y = − sin x from x
= 0 to x = π.
a) Draw the solid obtained by rotating this region about the
line x = 2π.
b) Which method (washers or shells) is preferable for finding
the volume of this solid? Explain.
c) Determine the volume of the solid

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

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...

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

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)...

Find the volume V of the solid obtained by rotating the region
bounded by the given curves about the specified line. 2x = y^2, x =
0, y = 5; about the y-axis
sketch the region, sketch the solid

Find the area of the region bounded by the parabola y = 1 + 2x -
x^2 and the parabola y = 1 + x^2. Please show the steps involved to
obtain the boundaries.
Please be legible and do not use cursive. Please show all work,
including ALL algebra. Thank you for your help!

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

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