7.1 – 7.3 review area and volume. the function v(t) is the velocity in m/sec of a particle moving...
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7.1 – 7.3 Review
Area and Volume
20 ,sincos5 .1 2 ttttv
The function v(t) is the velocity in m/sec of a particle moving along the x-axis. Determine when the particle is moving to the right, to the left, and stopped.
2. The velocity in m/sec of a particle moving along the x-axis is given by the function
Find the particle's displacement for the given time interval. If s(0) = 3, what is the particle's final position at the end of the given time interval?
40 ,51
102
tt
ttv
160 ,16 .3 tttv
The function v(t) is the velocity in m/sec of a particle moving along the x-axis. Find the total distance traveled by the particle.
4. A car accelerates from rest at the rate of mph per second for 16 seconds. What is its velocity after 16 seconds?
t25.1
5. In town A , the birth rate is given by
where t is the number of years since 1990. In town B , the birth rate is given by
where t is the number of years since 1990. How many more births are there in town B than in town A during the 1990s (from t = 0 to t = 10)? Round your answer to the nearest whole number.
year)per (births 53 12.0 tetb
year)per (births 86 43.0 tetB
6. It took 1930 J of work to stretch a spring from its natural length of 1 m to a length of 3 m. Find the spring's force constant.
4 ;62 .7 22 xyxxyFind the area of the shaded region.
22 ;68 .8 xyxy Find the area of the shaded region.
64 where,328 ;2 .9 2 xxyxyFind the area of the regions enclosed by the lines and curves.
.04 ;0 .10 3 yxyxFind the area enclosed by the given curves.
4 ;21 .11 2 yxyxFind the area of the regions enclosed by the lines and curves.
4
3 ;
6
sin .12
xy
xy
Find the area of the region(s) enclosed by the given curves.
Find the volume of the described solid.13.The solid lies between planes perpendicular to the x-axis at x =
3 and x = 3 and . The cross sections perpendicular to the x-axis between these planes are squares whose bases run from the semicircle to the semicircle
29 xy .9 2xy
xy 5
Find the volume of the solid generated by revolving the shaded region about the given axis.
14. About the y-axis
5 ,0 ,0 ,25 .15 2 xxyxy
Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the .
54 ,5 .16 2 xyxy
Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the .
,3xy
Find the volume of the solid generated by revolving the region about the y-axis.
17.The region in the first quadrant bounded on the left by on the right by the line x = 2, and below by the x-axis.
axis about the .18 y
Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated line.
xy 33x
6 line about the .19 y
Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated line.
2yx
6yx
0 ,8 .20 2 xyyx
Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the x-axis.