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100

Integrate ∫(4x2+x+3)dx

What is 4/3x3+x2/2+3x+C

100
Use the Fundamental Theorem of Calculus to evaluate ∫(3+x)dx on [0,8]
What is 56
100

Integrate ∫[x2/(sqrt(x3+3))]dx

What is 2/3 sqrt(x3+3)+C

100
Use a right endpoint rectangular model to estimate the area under the curve f(x)=x^2 between x = 0 and x = 3 using 6 rectangles of equal width
What is 11.375
100
Find the volume: The solid lies between planes perpendicular to the x-axis at x = -4 and x = 4. The cross sections perpendicular to the x-axis are circular disks whose diameters run from the parabola y = x² to the parabola y = 32 - x²
What is 16384/15 * π
200

Integrate ∫(2x - 9sin⁡x )dx

What is x2 + 9cosx+C

200

Use the Fundamental Theorem of Calculus to evaluate ∫(4x3-2x)dx on [-1,1].

What is 0

200

Integrate ∫[x(1-3x2)4]dx

What is (-1/30)(1-3x2)5 +C

200
Find the total area of the region between the y= 2x + 7 and the x-axis from x = 1 to x = 5.
What is 52
200
Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. y = √x, y = 0, x = 0, x = 9
What is V = 81/2 * π
300

Integrate ∫(t+et )dt

What is t2/2+et+C

300

Use the Fundamental Theorem of Calculus to find the derivative of the integral d/dx∫(sin t) dt on [0,x5]

5x4 * sin(x5)

300

Integrate ∫[(sinx)3cosx]dx

What is (1/4)(sinx)4+C

300
Find the area of the total region enclosed by the curves f(x) = x³+x²-6x and g(x) = 6x
What is 937/12
300
Find the volume of the solid generated by revolving the region bounded by the curves about the x-axis. y = -6x + 12, y = 6x, x = 0
What is 72π
400

Integrate ∫(10/x) dx

What is 10ln|x| + C

400
Use the Fundamental Theorem of Calculus to evaluate ∫(3/x)dx on [1,6]
What is 3ln(6)
400

Integrate ∫[xe-3x^2]dx

What is (-1/6)e-3x^2+C

400
Find the area enclosed by the curves y = 2x - x² and y = 2x - 4
What is 32/3
400
Find the volume of the solid generated by revolving the region about the y-axis. The region in the first quadrant bounded on the left by y = x³, on the right by the line x = 4, and below by the x-axis.
What is 2048/5 * π
500

Integrate ∫[6(5x) dx]

What is 6(5x)/ln(5) + C

500

Use the Fundamental Theorem of Calculus to evaluate ∫x(x2-6)dx on [-2,1]

What is 21/4

500

Integrate ∫[(x2 + 16)1/2]/(x4) dx

What is −[(x2+16)3/2]/(48x3)+C

500
Find the area enclosed by the curves y = x and y = x²
What is 1/6
500
The region shown is to be revolved about the x-axis to generate a solid. Which of the methods (disk/washer, shell) could you use to find the volume of the solid? How many integrals would be required in each case?
Washer+Disk (2 integrals), Shell (1 integral)