AP Calculus AB :Unit 8 — Applications of Integration Practice Test

What is the average value of √ x on the interval [5, 12] ?

Divya received the following problem:
A particle moves in a straight line with velocity v ( t )= √ 3 t−1 meters per second, where t is time in seconds. At t=2 , the particle’s distance from the starting point was 8 meters in the positive direction. What is the particle’s position at t=7 seconds?
Which expression should Divya use to solve the problem?

The population of a town grows at a rate of r (t) people per year (where t is time in years). At t=3 , the town’s population was 1000 people. What does    mean?

What is the area of the region between the graphs of f ( x )=8 x +6 and  g ( x ) =x−x ² from x=−6 to x=−1 ?

The curves x=7 y +18 and x=2 y 2 +19 y +18 are graphed. Which expression represents the area bounded by the curves?

Let f ( x )=x 3 + x 2 −6 x and  let R and S be two regions enclosed by the graphs of f and g as shown in the graph. Find the sum of the areas of regions R and S  decimal places.

Let R be the region enclosed by the graphs of functions f and g .Region R is the base of a solid whose cross sections perpendicular to the x -axis are squares. Which one of the definite integrals gives the volume of the solid?

The base of a solid S is the region bounded by the graphs of the functions and g shown below. f Cross-sections perpendicular to the x -axis are semi-circles. Which one of these integrals represents the volume of solid S ?

Let R be the region in the first quadrant enclosed by the axis, the line y=2 , and the curve y= √ 9−x² A solid is generated by rotating R aboout the – y axis What is the volume of of terms of π ?

Let R be the region enclosed by the line x=1  , the line y=2 , the line y=4 , and the curve y=( x−1 ) ² . A solid is generated by rotating R about the line x=1 the solid in terms of π ?

Region in the first quadrant is enclosed by the -axis, the line , and the curve .

What is the volume of the solid generated when is rotated about the -axis in terms of ?

Let be the region enclosed by the curves and .

A solid is generated by rotating about the line . What is the volume of the solid in terms of ?

A particle moves along the x -axis with velocity v ( t )=ln( t ² +5 t+1) . What is the particle’s displacement between the times t=1 and t= 5 your answer to three decimal places.

What is the average value of ³√ 3 x on the interval −5 ≤ x ≤ 9 ?

Determine the volume of the region bounded by y=x² −2 x and y=x that is rotated about y=4

What integral would allow you to find the volume of the region bounded by y=2 x ² and y=8 around the line y=11 .

Write the integral that would be used to find the area bounded by the graphs of and .

If the region enclosed by y=3 x ² , y=3 is revolved about the x- axis what is  the volume of the solid generated?

Find the area of the region bounded by the graphs of y=x 2 and y=4 x .