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24 Cards in this Set
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What is the Anti Power Rule?

that the antiderivative of x to the nth power is:
x to the n+1 quantity over n+1 

AD of cos ax?

1/a * sinax + C


AD of sin ax?

1/a * cosax + C


AD of sec^2(ax)

1/a * tanax + C


AD of csc^2(ax)

1/a * cotax +C


AD of sec(ax)tan(ax)?

1/a * secax + C


AD of cos(ax)cot(ax)

1/a * cscax + C


AD of e^ax

1/a * e^ax + C


AD of b^x

1/(lnb) * b^x + C


AD of 1/x

ln x


AD of 1/(sqrt(a^2x^2))

ARCSIN(x/a)


AD of 1/(a^2+x^2)

ARCTAN(x/a)


AD of a/(x*sqrt(x^2a^2))

1/a * ARCSEC( x/a ) + C


a~b f(x)dx = ? (Reiman's Sum)

limit as n approaches ∞ of the summation (k=1,n) of f(X˚K) times the ∆x. X˚K is any point between X K1 and X K.


what happens if you flip the endpoints of an integral?

flip the sign of the integral.


how can you split a summation?

∑(k=1,n) = ∑(k=1,a) + ∑(k=a+1,n)


What is the fundamental theorm of calculus (part 1)

if cont, A(x) = a~x f(t)dt (a≤x≤b),
then A'(x) = f(x) 

d/dx of A(g(x))=a~g(x) f(t)dt

A'(g(t)) *g'(t)


What is the fundamental theorm of calculus part 2?

a~b f(x)dx = F(b)F(a)
where F(x) is the antiderivative of f(x) 

a~a and f is even?

= 2 * 0~a f(x)dx


a~a and f is odd?

0


How to find the average value of a function on an interval?

1/(ba) * a~b f(x)dx


the substitution rule for indefinate integrals.

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)


substitition for definate integrals

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)
