The integral used to find the area bounded by y = 2^x , y = 8, and the y-axis. (Must include a sketch of the region)
What is Int(8 - 2^x,x,0,3)
100
The integral used to compute the volume of the solid obtained by rotating the region enclosed by y = x^3 and y = 4x about the x-axis.
What is pi * Int(16x^2 - x^6,x,0,2)
100
The integral used to find the volume of the solid obtained by rotating the region bounded by the graphs of y = sqrt(x),
y = 2 − x and y = 0 around the x-axis. (You must sketch the region.)
What is pi * Int((2 - x)^2 - x,x,0,1)
100
Suppose a force of 10 N is required to stretch a spring 0.1 m from its equilibrium position and hold it in that position. How much work is need to stretch the spring 0.25 m from its equilibrium position?
What is 3.125 J
100
Determine the average value of the function f(t) = t^2 - 5t + 6cos(pi*t) on the interval [-1,5/2].
What is -1.62
200
The integral used to find the area bounded by y = 3^x , x = 2, the x-axis, and the y-axis. (Must include a sketch of the region.)
What is Int(3^x,x,0,2)
200
The integral used to compute the volume of the solid obtained by rotating the region enclosed by y = x^3 and y = 4x about y = -1.
What is pi * Int((4x + 1)^2 - (x^3 + 1)^2,x,0,2)
200
The integral used to find the volume obtained by revolving the region bounded by y = x^2 − 4 and y = 4 − x^2 around
the line x = 2? (You must sketch the region.)
What is 2pi * Int((2 - x)((4 - x^2) - (x^2 - 4)),x,-2,2)
200
Archaeologists have determined that the Great Statue of Aruba was really a giant magnet placed on top of an
iron table. At a height of x feet above the table, the magnetic force exerted on the statue
was given by F(x) = 1600/(2x + 1)^2 lb. When the mighty Hercules lifted the statue 3 feet before hurling it at Ares, how much work did he do? (You
may ignore gravity; the statue was hollow and had very little mass.)
What is 4800/7 ft-lbs
200
Determine the average value of the function R(z) = sin(2z)e^(1 - cos(2z)) on the interval [-pi,pi].
What is 0
300
The integral used to find the area in the first quadrant between x^2 + y^2 = 1 and x^(1/2) + y^(1/2) = 1. (Must include a sketch of the region.)
What is Int(sqrt(1-x^2) - (1 - sqrt(x))^2,x,0,1)
300
The integral used to compute the volume of the solid obtained by rotating the region enclosed by y = x^3 and y = 4x about y = 9
What is pi * Int((9 - x^3)^2 - (9 - 4x)^2,x,0,2)
300
The integral used to find the volume of the solid obtained by rotating the area between the graphs of y = x^2 and x = 2y
around the y-axis. (You must sketch the region.)
What is
Shell: 2pi * Int(x(x/2 - x^2),x,0,1/2)
Washer: pi * Int(y - 4y^2,y,0,1/4)
300
A bucket that weighs 70 lb when filled with water is lifted at a constant rate, by a mechanical winch, from the
bottom of a well that is 60 feet deep. The chain that is being used to lift the bucket weighs 0.55 pounds per foot.
Now find the amount of work required to lift the bucket from the bottom of the well all the way to
the top.
What is 5,190 ft-lbs
400
The integral used to find the area between the curves
y = cos(x) and y = 1/2 x - 1, bounded on the left by the y-axis. Use technology to find the point of intersection rounded to 3 decimal places. (Must include a sketch of the graph.)
What is Int(cosx - (1/2 x - 1),x,0,1.714)
400
The integral used to compute the volume of the solid obtained by rotating the region enclosed by y = x^3 and y = 4x about the y-axis.
What is pi * Int(y^(2/3) - (y/4)^2,y,0,8)
400
Integral used to find the volume of the solid obtained by rotating the region between the graphs of y = x sqrt(2 - x) and y = 0 around the x-axis. (You must sketch the region.)
What is pi * Int(2x^2 - x^3,x,0,2)
400
It takes 100 J of work to stretch a spring 0.5 m from its equilibrium position. How much work is needed to stretch it an additional 0.75 m?
What is 525 J
500
The integral used to find The area bounded by the curves y = x^2 - 4 and y ={ 1/2 x + 1 if x <= 0, -1/2 x + 1 if x > 0 (Must include sketch of graph)
What is Int((1/2 x + 1) - (x^2 - 4),x,-2,0) + Int((-1/2 x + 1) - (x^2 - 4),x,0,2)
500
The integral used to compute the volume of the solid obtained by rotating the region enclosed by y = x^3 and y = 4x about x = 2.
What is pi * Int((2 - y/4)^2 - (2 - y^(1/3))^2,y,0,8)
500
The Integral used to find the volume formed by rotating the region enclosed by y = 2x - x^2 and the x-axis about the line x = -1. (You must sketch the region.)
What is 2pi * Int((x+1)(2x - x^2),x,0,2)
500
A cylindrical tank with a length of 10 m and a radius of 5 m is on its side and half-full of gasoline. How much work is required to empty the tank through an outlet pipe at the top of the tank? (The density of gasoline is 737 kg/m^3)