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.