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7.1 – 7.3 Review Area and Volume

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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.

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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?

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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.

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4.A car accelerates from rest at the rate of mph per second for 16 seconds. What is its velocity after 16 seconds?

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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.

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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.

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Find the area of the shaded region.

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Find the area of the regions enclosed by the lines and curves.

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Find the area enclosed by the given curves.

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Find the area of the regions enclosed by the lines and curves.

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Find the area of the region(s) enclosed by the given curves.

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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

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Find the volume of the solid generated by revolving the shaded region about the given axis. 14. About the y-axis

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Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the.

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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.

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Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated line.

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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.

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