# 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.
1 of 31
Gradient of a curve given parametrically
dy/dx = dy/dt // dx/dt
2 of 31
When y=a^x
dy/dx = a^x lna
3 of 31
In vectors, if a and b are parallel
then a.b = |a| |b|, in particular a.a = |a|^2
4 of 31
The acute angle x between two straight lines
cos x = | a.b / |a| |b| | where a and b are direction vectors of the lines
5 of 31
Integrate x^n
= x^n+1 / n+1 +C
6 of 31
Integrate e^x
= e^x +C
7 of 31
Integrate 1/x
= ln |x| +C
8 of 31
Integrate cosx
= sinx +C
9 of 31
Integrate sinx
= -cosx +C
10 of 31
Integrate sec^2x
= tanx +C
11 of 31
Integrate cosecx cotx
= -cosecx +C
12 of 31
Integrate cosec^2x
= -cotx +C
13 of 31
Integrate secxtanx
= secx +C
14 of 31
Integrate (ax + b)^n dx
= 1/a times (ax + b)^n+1 // n + 1 +C
15 of 31
Integrate e^ax+b dx
= 1/a e^ax+b +C
16 of 31
Integrate 1/ax + b dx
= 1/a ln|ax + b| +C
17 of 31
Integrate cos(ax + b) dx
= 1/a sin(ax + b) +C
18 of 31
Integrate sin(ax + b) dx
= -1/a cos(ax + b) +C
19 of 31
Integrate sec^2(ax + b) dx
= 1/a tan (ax + b) +C
20 of 31
Integrate cosec(ax + b) cot(ax + b) dx
= -1/a cosec (ax + b) +C
21 of 31
Integrate cosec^2 (ax + b) dx
= -1/a cot (ax + b) +C
22 of 31
Integrate sec(ax + b) tan(ax + b) dx
= 1/a sec (ax + b) +C
23 of 31
Integration by parts
Integrate u dv/dx dx = uv - integrate v du/dx dx
24 of 31
Integrate tanx dx
= ln |secx| +C
25 of 31
Integrate secx dx
= ln |secx + tanx| +C
26 of 31
Integrate cotx dx
= ln |sinx| +C
27 of 31
Integrate cosecx dx
= -ln |cosecx + cotx| +C
28 of 31
Trapezium rule
1/2 h [y0 + 2(y1 + y2 + y3 + ... + y n-1) + yn where h= b-a // n
29 of 31
Area
Integrate between b and a y dx
30 of 31
Volume
pi times integral of y^2 dx between b and a
31 of 31

## Other cards in this set

### Card 2

#### Front

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

#### Back

Gradient of a curve given parametrically

dy/dx = a^x lna

### Card 4

#### Front

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

### Card 5

#### Front

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

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