Area and Distance Integral Calculus

The graph of the function f shown above consists of two line segments and a semicircle. Let g be defined by the above integral. What is the value of g(5)?

• 0

• -1.5 + 2π

• 2π

• 1.5 + 2π

• 4.5 + 2π

Let f and g be continuous functions such that the above is true. Find the above value.

• 3

• 7

• 11

• 15

• 19

For time t ≥ 0, the position of a particle traveling along a line is given by a differentiable function s. If s is increasing for 0 ≤ t < 2 and s is decreasing for t > 2, which of the following is the total distance the particle travels for 0 ≤ t ≤ 5?

• 
• 
• 
• 
• 

The table above gives selected values for a continuous function f. If f is increasing over the closed interval [0, 3], what does the above integral equal?

• 50

• 62

• 77

• 100

• 154

What is the volume of the solid generated when the region bounded by the graph of the above equation and the lines x = 0 and y = 5 is revolved about the y-axis?

• 3.464

• 4.500

• 7.854

• 10.883

• 14.137

The function f is continuous. Use the top integral to help determine the bottom integral.

• 1.5

• 3

• 6

• 12

• 24

If the above is an antiderivative for f(x), then determine the above integral.

• -0.281

• -0.102

• 0.102

• 0.260

• 0.282

A vase has the shape obtained by revolving the curve y = 2 + sin x from x = 0 to x = 5 about the x-axis, where x and y are measured in inches. What is the volume, in cubic inches, of the vase?

• 10.716

• 25.501

• 33.666

• 71.113

• 80.115

At time t = 0 years, a forest preserve has a population of 1500 deer. If the rate of growth of the population is modeled by R(t) = 2000e^0.23t deer per year, what is the population at time t = 3?

• 3987

• 5487

• 8641

• 10,141

• 12,628

Let f and g be continuous functions. Use the three above integrals to solve for the bottom one.

• -23

• -19

• -17/2

• 19

• 23