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Integrals
Derivatives
Areas
Volumes
Random Calculus Fun
100
The derivative of cos(4x)/4
What is -sin(4x)dx?
100
The integral of x54813548
What is x54813549/54813549 + C ?
100
The area above the x axis and below the graph of y=x2 from -4 to 4
What is 42.6666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666?
100
The volume of y=x rotated around the x axis from 0 to 2
What is 2 and 2 thirds pi?
100
Derivative of the integral of the function equals the function.
What is the Fundamental Theorem of Calculus?
200
The derivative of .25x4+9x3+x2+.125x+12
What is (x3+27x2+2x+0.125)dx?
200
The integral of ln2x
What is 2/x + C ?
200
The total area between the x axis and the graph of y=21sin(2x) from -π/2 to π/2
What is 42?
200
The volume of y=x2 rotated around the x axis from -2 to 2
What is 12.8 or 64/5
200
The limit as h approaches 0 of [f(x+h)-f(x)]/h
What is the definition of a derivative?
300
The derivative of 2sin-1(x)
What is [2/(sqrt(1-x2))]dx?
300
The integral of sin(.25x)/4
What is -cos(.25x) + C ?
300
The area between the function y=x and the y axis from -4 to 10
What is 42?
300
The volume of y=1/x2 rotated around the x axis from .5 to 1
What is two and a third pi?
300
f'(c)=[f(b)-f(a)]/(b-a)
What is the mean value theorem?
400
The derivative of 4e.25x
What is e.25xdx?
400
The integral of x3+36x2+12x+1
What is 4x4+12x3+24x2+x+C ?
400
The area between the graph of 7/x2 and the x axis from -1 to -.5
What is 7?
400
V=(4/3)πr3
What is the volume of a sphere?
400
The derivative of the inside of a function multiplied by the derivative of the outside. (f o g)'=(f' o g)g'
What is the chain rule?
500
The derivative of xsin(x)
What is [sin(x)+xcos(x)]dx?
500
The integral of tan-1(25x)
What is 25/(625x2+1) + C ?
500
The total area between the x axis and the graph of x3 from -2 to 2
What is 8?
500
The volume of the area between y=x and y=x.5 rotated around the x axis from 0 to 3
What is 14/3 or 4.667
500
L(x) = f(a) + f'(a)(x − a)
What is the linearization of a function f(x) at a point a?