Question

Write and evaluate the definite integral that represents the
volume of the solid formed by revolving the region about the
*y*-axis.

* y* =

squareroot of 16
− x^{2} |

going from upper 9,lower4.

Answer #1

1. Use the shell method to set up and evaluate the integral that
gives the volume of the solid generated by revolving the plane
region about the line x=4.
y=x^2 y=4x-x^2
2. Use the disk or shell method to set up and evaluate the
integral that gives the volume of the solid generated by revolving
the region bounded by the graphs of the equations about each given
line.
y=x^3 y=0 x=2
a) x-axis b) y-axis c) x=4

Write and evaluate the definite integral that represents the
area of the region bounded by the graph of the function and the
tangent line to the graph at the given point. f(x) = 5x^3 − 3, (1,
2)

Use a detailed analysis to set up but not evaluate an integral
for the volume Z of the solid generated by revolving the region
bounded by the curves 2x = y^2, x = 0, and y = 4 about the
y-axis.

Set up the integral (do not evaluate) to find the volume of the
solid generated by revolving the region about the line x=5.
The region is bounded the graphs x=y^2, x=4
Use the disk and shell methods.

Find the volume of the solid generated by revolving the region
about the given line.
The region in the second quadrant bounded above by the curve y =
9 - x^2 , below by the x-axis, and on the right by the y-axis,
about the line x=1.
Please write as legible as possible and thanks for the help.

Set up, but do not evaluate, the integral for the volume of the
solid obtained by rotating the region enclosed by y=\sqrt{x}, y=0,
x+y=2 about the x-axis. Sketch
a) By Washers
b) Cylindrical shells

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.

Find the volume of the solid generated by revolving the following
region about the given axis. The region in the first quadrant
bounded above by the curve y=x^2, below the x-axis, and on the
right by the line x=1, about the line x=-4. Use the washer method
to set up the integral that gives the volume of the solid.

Find the volume of the solid generated by revolving the region
bounded by the graphs of y = e x/4 , y = 0, x = 0, and x = 6 about
the x−axis.
Find the volume of the solid generated by revolving the region
bounded by the graphs of y = √ 2x − 5, y = 0, and x = 4 about the
y−axis.

Determining Volumes by the Disk-Washer Method
1. Find the volume of the solid formed by revolving the region
bounded by the graph of f(x) = √sin(x) and the x−axis from 0 ≤ x ≤
π about the x−axis. [f(x)= square root(sin(x))]

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