Integrals
Derivatives
Theorems
Differentiation Rules
Area/Volume/Etc.
100
sin x dx
What is -cos x + C?
100
sin x
What is cos x?
100
If f is continuous on [a, b], differentiable on (a, b), and f(a) = f(b), then there exists a number c in (a, b) such that f'(c) = 0.
What is Rolle's Theorem?
100
(fg)' = fg' + gf'
What is the Product Rule?
100
(pi)fnint(R^2, x, a, b)
What is the disk method?
200
k dx
What is kx + C?
200
e^x
What is e^x?
200
If f is continuous on [a, b] and differentiable on (a, b), then there exists a number c in (a, b) such that f'(c) = [f(b) - f(a)]/(b-a).
What is the Mean Value Theorem?
200
(f/g)' = (gf' - fg')/g^2
What is the Quotient Rule?
200
fnint(Top - Bottom, x, a, b)
What is area?
300
sec x tan x dx
What is sec x + C?
300
cot x
What is -csc^2 x?
300
If f is continuous and differentiable on (a, b), then there is a number c such that f(c) = 1/(b - a)fnint(f(x), x, a, b).
What is the average value of a function?
300
[f(u)]' = f'(u)u'
What is the Chain Rule?
300
(pi)fnint(R^2 - r^2, x, a, b)
What is the washer method?
400
csc x cot x dx
What is -csc x + C?
400
ln u
What is u'/u?
400
fnint(f(x), x, a, b) = F(b) - F(a)
What is the Fundamental Theorem of Calculus?
400
(ln a)(a^u)u'
What is the derivative of a^u?
400
fnint(area, x , a, b)
What is the volume of a solid with known cross sections?
500
1/(1 + x^2)
What is arctan x + C
500
arcsin x
What is 1/sqrt(1 - x^2)?
500
If f is continuous on [a, b], then for any number c between f(a) and f(b) , there exists a number d in the open interval (a, b) such that f(d) = c.
What is the Intermediate Value Theorem?
500
(f^-1)'(x) = 1/[f'(f^-1(x))]
What is the derivative of an inverse function?
500
left, right, midpoint, trapezoidal
What is a kind of sum (Reimann sum)?
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