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Va-Va-Volumes
100
Integrate ∫(4x^2+x+3)dx
What is 4/3x^3+x^2/2+3x+C
100
Use the Fundamental Theorem of Calculus to evaluate ∫(3+x)dx on [0,8]
What is 56
100
Integrate ∫[x^2/(sqrt(x^3+3))]dx
What is 2/3 sqrt(x^3+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-9 sin⁡x )dx
What is x^2 + 9cosx+C
200
Use the Fundamental Theorem of Calculus to evaluate ∫(4x^3-2x)dx on [-1,1].
What is 0
200
Integrate ∫[x(1-3x^2)^4]dx
What is (-1/30)(1-3x^2)^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+e^t )dt
What is t^2/2+e^t+C
300
Use the Fundamental Theorem of Calculus to find the derivative of the integral d/dx∫(sin t) dt on [0,x^5]
5x^4 * sin(x^5)
300
Integrate ∫[(sinx)^3*cosx]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(5^x) dx]
What is 6(5^x)/ln(5) + C
500
Use the Fundamental Theorem of Calculus to evaluate ∫x(x^2-6)dx on [-2,1]
What is 21/4
500

Integrate ∫[(x^2 + 16)^1/2]/(x^4) dx

What is −[(x^2+16)^(3/2)]/(48x^3)+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)