C4 Integration Techniques Summary of the techniques used in integration 2.0 / 5 based on 2 ratings ? MathematicsCalculusAlgebra and functionsIntegrationA2/A-levelEdexcel Created by: emma louiseCreated on: 18-05-14 14:47 Integration of e^x and 1/x e^x ne^kx => n/k.e^kx 1/x n/kx => n/k.ln|x| 1/nx+k => 1/n . ln|nx+k| 1 of 9 Integration of sin and cos sinx => -cosx + c cosx => sinx + c sec^2x => tanx + c ------------------------------------------------------------------- cosecxcotx => -cosecx + c secxtanx => secx + c cosec^2x => -cotx + c 2 of 9 Integration of f'(x)/f(x) If the differential is on top then it becomes ln of the denominator ~f'(x)/f(x) => ln|f(x)| 3 of 9 Integration by Substitution Allow something to equal 'u' Integrate Substitute the 'u' value back in at the end -DO NOT FORGET to change dx to du by differentiating u and rearranging 4 of 9 Integration by Parts This is the reverse of the product rule ʃ(u.dv/dx)dx => uv - ʃ(v.du/dx)dx This is how you would integrate ln|x| let u = lnx let dv/dx = 1 find du/dx and v to use above formula 5 of 9 Tough Integrals REMEMBER YOU CAN USE: -Trigonometric Identities -Partial Fractions -Some integrals are given in the formula booklet 6 of 9 Volumes of Revolution V = πʃ(y^2) dx with x limits FOR PARAMETRIC V = πʃ(y.dx/dt) dt with t limits They may not give the limits as t so you will need to change them 7 of 9 Differential Equations Get x's and y's on the same side dy/dx = yx => 1/y dy = x dx DON'T FORGET after integrating both sides, put C on one of them (c is a constant so doesn't need to be on both sides) 8 of 9 Trapezium Rule h/2[y0+yn+2(y1+y2+...yn-1)] h is width of *****, h=(b-a)/n GIVEN FORMULA % ERROR =[(exact value-approximate value)/exact value] x 100 9 of 9
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