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Last updated 12:05 AM on 3/2/23
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22 Terms
1
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csc^2(x)
-cot(x)
2
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csc(x)cot(x)
-csc(x)
3
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save -sin(x) convert to cos
odd sin exp
4
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save cos(x) convert to sin
odd cos exp
5
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even powers
half/double angle id
6
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sin(mx)cos(nx) or variations
sum/diff ids
7
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save sec^2(x) covert to tan
even sec exp
8
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save sec(x)tan(x) convert to sec
odd tan exp
9
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convert to sec no factors saved
even tan/odd sec
10
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sqrt(a^2-x^2)
u\=asin(theta)
11
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sqrt(a^2+x^2)
u\=atan(θ)
12
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√(x^2-a^2)
u\=asec(θ)
13
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Right Endpoint Rule
(Δx)(f(x1)+f(x2)...(f(xn))
14
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Left endpoint
(Δx)(f(x0)+f(x1)...f(x-1))
15
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Midpoint Rule
Δx (f((x1+x2)/2)
16
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Trapezoidal Rule
((Δx)/2)(f(x0)+2f(x1)+2f(x2)...+2f(xn-1)+f(xn))
17
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Simpsons Rule
((Δx)/3)(f(x0)+4f(x1)+2f(x2)+4f(x3)+2f(x4)...+4f(xn-1)+f(xn))
18
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Cyl shells abt y or x\=
2pi(x)(f(x)) x\=rad, or f(x)-g(x)
19
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Cyl shells abt x or y\=
2pi(y)g(y) y =rad
20
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Arc Length
sqrt(1+(f'(x))) or sqrt((dx/dt)^2+(dy/dt)^2)
21
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SA abt x or y\=
2pif(x)sqrt(1+(f'(x))) or 2piysqrt(1+(f'(y))) or 2piy(t)sqrt((dx/dt)^2+(dy/dt)^2)
22
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Polar area
1/2(f(theta))^2