1. The amount of work to pump the water out of a half-full cylinder is half the amount of work to pump the water out of the full cylinder.

2. If the force is constant, the amount of work to move an object from [latex]x=a[/latex] to [latex]x=b[/latex] is [latex]F(b-a).[/latex]

3. The disk method can be used in any situation in which the washer method is successful at finding the volume of a solid of revolution.

4. If the half-life of [latex]\text{seaborgium-}266[/latex] is 360 ms, then [latex]k=\dfrac{(\text{ln}(2))}{360}.[/latex]

5. The volume that has a base of the ellipse [latex]\dfrac{{x}^{2}}{4}+\dfrac{{y}^{2}}{9}=1[/latex] and cross-sections of an equilateral triangle perpendicular to the [latex]y\text{-axis}\text{.}[/latex] Use the method of slicing.

6. [latex]y={x}^{2}-x,[/latex] from [latex]x=1\text{ to }x=4,[/latex] rotated around the [latex]y[/latex]-axis using the washer method

7. [latex]x={y}^{2}[/latex] and [latex]x=3y[/latex] rotated around the [latex]y[/latex]-axis using the washer method

8. [latex]x=2{y}^{2}-{y}^{3}, x=0,\text{ and }y=0[/latex] rotated around the [latex]x[/latex]-axis using cylindrical shells

9. [latex]y={x}^{3},x=0,y=0,\text{ and }x=2[/latex]

10. [latex]y={x}^{2}-x\text{ and }x=0[/latex]

11. [T] [latex]y=\text{ln}(x)+2\text{ and }y=x[/latex]

12. [latex]y={x}^{2}[/latex] and [latex]y=\sqrt{x}[/latex]

13. [latex]y=5+x[/latex], [latex]y={x}^{2}[/latex], [latex]x=0[/latex], and [latex]x=1[/latex]

14. Below [latex]{x}^{2}+{y}^{2}=1[/latex] and above [latex]y=1-x[/latex]

15. Find the mass of [latex]\rho ={e}^{\text{−}x}[/latex] on a disk centered at the origin with radius 4.

16. Find the center of mass for [latex]\rho ={ \tan }^{2}x[/latex] on [latex]x\in (-\frac{\pi }{4},\frac{\pi }{4}).[/latex]

17. Find the mass and the center of mass of [latex]\rho =1[/latex] on the region bounded by [latex]y={x}^{5}[/latex] and [latex]y=\sqrt{x}.[/latex]

18. The length of [latex]x[/latex] for [latex]y=\text{cosh}(x)[/latex] from [latex]x=0\text{ to }x=2.[/latex]

19. The length of [latex]y[/latex] for [latex]x=3-\sqrt{y}[/latex] from [latex]y=0[/latex] to [latex]y=4[/latex]

20. The shape created by revolving the region between [latex]y=4+x[/latex],  [latex]y=3-x[/latex],  [latex]x=0[/latex],  and [latex]x=2[/latex] rotated around the [latex]y[/latex]-axis.

21. The loudspeaker created by revolving [latex]y=\dfrac{1}{x}[/latex] from [latex]x=1[/latex] to [latex]x=4[/latex] around the [latex]x[/latex]-axis.

22. Find the total force on the wall of the dam.

23. You are a crime scene investigator attempting to determine the time of death of a victim. It is noon and [latex]45\text{°}\text{F}[/latex] outside and the temperature of the body is [latex]78\text{°}\text{F}.[/latex] You know the cooling constant is [latex]k=0.00824\text{°}\text{F/min}\text{.}[/latex] When did the victim die, assuming that a human’s temperature is [latex]98\text{°}\text{F}[/latex]?

24. [T] The best-fit exponential curve to these data is given by [latex]y=40.71+{1.224}^{x}.[/latex] Why do you think the gains of the market were unsustainable? Use first and second derivatives to help justify your answer. What would this model predict the Dow Jones industrial average to be in 2014?

25. Find the volume of the catenoid [latex]y=\text{cosh}(x)[/latex] from [latex]x=-1\text{ to }x=1[/latex] that is created by rotating this curve around the [latex]x\text{-axis},[/latex] as shown here.

26. Find surface area of the catenoid [latex]y=\text{cosh}(x)[/latex] from [latex]x=-1[/latex] to [latex]x=1[/latex] that is created by rotating this curve around the [latex]x\text{-axis.}[/latex]