Question

- Let R in the x,y-plane be in the first quadrant and bounded by
*y=x+2 and y=**x**2*, and x = 0. Find the volume generated by revolving the region R about the line x = 4.

Answer #1

Find the volume of the solid generated by revolving the region
bounded by
x2−y2=16, x≥0, y=−4,y=4
about the line
x=0.

Let R be the region bounded by 6 cos x, y = e^x , x = 0, and ?
=pi /2 . Using a method of your choice, find the volume of the
solid generated by revolving R around the line y = 7. Give an exact
numerical answer.

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 the curves y = x, y = x+ 2, x =
0, and x = 4. Find the volume of the solid generated when R is
revolved about the x-axis. In addition, include a carefully labeled
sketch as well as a typical approximating disk/washer.

PLEASE USE TWO dy-INTEGRALS
Let R be the region in the first quadrant bounded by the curves
y = f(x) = 2x+ 1 and y = g(x) = 2x 2 − 8x + 9. Find the
volume of the solid obtained by rotating the region R about y-axis
using two dy-integrals.

Find the volume generated by revolving the area in the first
quadrant bounded by the
curve y = e-x when the area is revolve about the line y
= -1 using the circular ring
method.

The region R is bounded by y=x^2 and y=sqrtx. Find the volume of
the solid generated by revolving R about
a) the x-axis b) the y-axis c) the line y=1 d) the line y=-1 e)
the line x=1 f) the line x=-1

Find the volume of the solid generated by revolving the region
bounded by y = 2x−x2 and y = x about; (a) the y-axis (b) the line
xr = 1.

Let R be the region bounded by y=ln(x), the x-axis, and
the line x=e. Find the volume of the solid that is generated when
the region R is revolved about the x-axis.

Find the volume of the solid generated by revolving the plane
region bounded by the graphs of y= \sqrt{x} , y=0, x=5, about the
line x=8.
Find the volume using: a) DISK/WASHER Method b) SHELL METHOD

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