C4 Formulas

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  • Created by: sarxhj
  • Created on: 12-04-15 19:46
Binomial Expansion of (1 + x)^n
= 1 + nx + n(n-1) x^2/2! + n(n-1)(n-2) x^3/3! ... etc.
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Gradient of a curve given parametrically
dy/dx = dy/dt // dx/dt
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When y=a^x
dy/dx = a^x lna
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In vectors, if a and b are parallel
then a.b = |a| |b|, in particular a.a = |a|^2
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The acute angle x between two straight lines
cos x = | a.b / |a| |b| | where a and b are direction vectors of the lines
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Integrate x^n
= x^n+1 / n+1 +C
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Integrate e^x
= e^x +C
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Integrate 1/x
= ln |x| +C
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Integrate cosx
= sinx +C
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Integrate sinx
= -cosx +C
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Integrate sec^2x
= tanx +C
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Integrate cosecx cotx
= -cosecx +C
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Integrate cosec^2x
= -cotx +C
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Integrate secxtanx
= secx +C
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Integrate (ax + b)^n dx
= 1/a times (ax + b)^n+1 // n + 1 +C
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Integrate e^ax+b dx
= 1/a e^ax+b +C
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Integrate 1/ax + b dx
= 1/a ln|ax + b| +C
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Integrate cos(ax + b) dx
= 1/a sin(ax + b) +C
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Integrate sin(ax + b) dx
= -1/a cos(ax + b) +C
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Integrate sec^2(ax + b) dx
= 1/a tan (ax + b) +C
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Integrate cosec(ax + b) cot(ax + b) dx
= -1/a cosec (ax + b) +C
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Integrate cosec^2 (ax + b) dx
= -1/a cot (ax + b) +C
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Integrate sec(ax + b) tan(ax + b) dx
= 1/a sec (ax + b) +C
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Integration by parts
Integrate u dv/dx dx = uv - integrate v du/dx dx
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Integrate tanx dx
= ln |secx| +C
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Integrate secx dx
= ln |secx + tanx| +C
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Integrate cotx dx
= ln |sinx| +C
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Integrate cosecx dx
= -ln |cosecx + cotx| +C
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Trapezium rule
1/2 h [y0 + 2(y1 + y2 + y3 + ... + y n-1) + yn where h= b-a // n
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Area
Integrate between b and a y dx
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Volume
pi times integral of y^2 dx between b and a
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Other cards in this set

Card 2

Front

dy/dx = dy/dt // dx/dt

Back

Gradient of a curve given parametrically

Card 3

Front

dy/dx = a^x lna

Back

Preview of the back of card 3

Card 4

Front

then a.b = |a| |b|, in particular a.a = |a|^2

Back

Preview of the back of card 4

Card 5

Front

cos x = | a.b / |a| |b| | where a and b are direction vectors of the lines

Back

Preview of the back of card 5
View more cards

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