Let R be the region bounded by the following curves. Let S be the solid generated when R is revolved about the given axis. If possible, find the volume of S by both the disk/washer and shell methods. Check that your results agree and state which method is easier to apply. y=

$$( x - 2 ) ^ { 3 }$$

-2, x=0, and y=25; revolved about the y-axis

Let R be the region bounded by the following curves. Let S be the solid generated when R is revolved about the given axis. If possible, find the volume of S by both the disk/washer and shell methods. Check that your results agree and state which method is easier to apply. y=

$$x^2$$

, y=2-x, and x=0 in the first quadrant; revolved about the y-axis.

Let R be the region bounded by the following curves. Let S be the solid generated when R is revolved about the given axis. If possible, find the volume of S by both the disk/washer and shell methods. Check that your results agree and state which method is easier to apply. y=x-

$$x^4$$

, y=0; revolved about the y-axis

Let R be the region bounded by the following curves. Let S be the solid generated when R is revolved about the given axis. If possible, find the volume of S by both the disk/washer and shell methods. Check that your results agree and state which method is easier to apply. y=x,

$$y=x^{1/3}$$

in the first quadrant; revolved about the x-axis

Disk method Let R be the region bounded by the following curves. Use the disk method to find the volume of the solid generated when R is revolved about the $x$-axis.
$y=4-x^2, y=0, x=0$

Let R be the region bounded by the following curves. Let S be the solid generated when R is revolved about the given axis. If possible, find the volume of S by both the disk/washer and shell methods. Check that your results agree and state which method is easier to apply. y=x-

$$x^4$$

, y=0; revolved about the x-axis

Let R be the region bounded by the following curves. Let S be the solid generated when R is revolved about the given axis. If possible, find the volume of S by both the disk/washer and shell methods. Check that your results agree and state which method is easier to apply. y=1/(x+1), y=1-x/3; revolved about the x-axis

Disks/washers about the $\boldsymbol{y}$-axis Let $R$ be the region bounded by the following lines and curves. Use the disk or washer method to find the volume of the solid generated when $R$ is revolved about the y-axis. \

$$y=0, y=\sqrt{x-1}, y=2, x=0$$

Let W be the region bounded by the planes $x = 0 , y = 0 , z = 0 , x + y = 1$ , and $z = x + y$ (a) Find the volume of W. (b) Evalute $\displaystyle \iiint _ { W } x d x d y d z$ (c) Evalute $\displaystyle \iiint _ { W } y d x d y d z$

You are making a scale model of a building. The front of the actual building is 60 ft wide and 100 ft tall. The front of your model is 3 ft wide and 5 ft tall. What is the scale factor of the reduction?

Find an equation of the tangent line to the circle at the indicated point. Recall from geometry that the tangent line to a circle is perpendicular to the radius of the circle at the point of tangency. Circle $x^{2}+y^{2}=12$ Point $(2,-2 \sqrt{2})$

Events A and B are independent. Find the missing probability.

$$P ( \mathrm { A } ) = \frac { 2 } { 5 }$$

,

$$P ( \mathrm { B } ) = \frac { 1 } { 6 }$$

, P(A and B)=___

Let R be the region bounded by the following curves. Use the disk or washer method to find the volume of the solid generated when R is revolved about the y-axis.

$$y = \sin ^ { - 1 } x$$

, x=0,

$$y = \pi / 4$$

Washer method Let R be the region bounded by the following curves. Use the washer method to find the volume of the solid generated when R is revolved about the x-axis.
$y=2 x, y=16 x^{1 / 4}$