C4 Formulas 4.0 / 5 MathematicsAll Core 4A2/A-levelEdexcel Created by: sarxhjCreated 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

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