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24 Cards in this Set
- Front
- Back
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What is the Anti Power Rule?
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that the antiderivative of x to the nth power is:
x to the n+1 quantity over n+1 |
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AD of cos ax?
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1/a * sinax + C
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AD of sin ax?
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1/a * -cosax + C
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AD of sec^2(ax)
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1/a * tanax + C
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AD of csc^2(ax)
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1/a * cotax +C
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AD of sec(ax)tan(ax)?
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1/a * secax + C
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AD of cos(ax)cot(ax)
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1/a * -cscax + C
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AD of e^ax
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1/a * e^ax + C
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AD of b^x
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1/(lnb) * b^x + C
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AD of 1/x
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ln |x|
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AD of 1/(sqrt(a^2-x^2))
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ARCSIN(x/a)
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AD of 1/(a^2+x^2)
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ARCTAN(x/a)
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AD of a/(x*sqrt(x^2-a^2))
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1/a * ARCSEC( |x/a| ) + C
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a~b f(x)dx = ? (Reiman's Sum)
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limit as n approaches ∞ of the summation (k=1,n) of f(X˚K) times the ∆x. X˚K is any point between X K-1 and X K.
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what happens if you flip the endpoints of an integral?
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flip the sign of the integral.
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how can you split a summation?
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∑(k=1,n) = ∑(k=1,a) + ∑(k=a+1,n)
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What is the fundamental theorm of calculus (part 1)
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if cont, A(x) = a~x f(t)dt (a≤x≤b),
then A'(x) = f(x) |
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d/dx of A(g(x))=a~g(x) f(t)dt
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A'(g(t)) *g'(t)
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What is the fundamental theorm of calculus part 2?
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a~b f(x)dx = F(b)-F(a)
where F(x) is the antiderivative of f(x) |
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-a~a and f is even?
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= 2 * 0~a f(x)dx
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-a~a and f is odd?
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0
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How to find the average value of a function on an interval?
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1/(b-a) * a~b f(x)dx
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the substitution rule for indefinate integrals.
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if u=g(x) were g' is a continuous on a,b and is a multiple of g, than the antiderivative of f(g(x))g'(x) is equal to the antiderivative of f(u)
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substitition for definate integrals
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if u=g(x) were g' is a continuous on a,b and is a multiple of g, than a~b f(g(x))g'(x) is equal to the g(a)~g(b) f(u)
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