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Integration workbookHow to use this workbookWhere to write your answersYou will see on each question there are one or more grey boxes. These are for you to type the answer in.Eg: 6 + 4 = FORMTEXT ?????In the box you write your answer.The layout keeps changingOne problem is that the grey boxes are a different size when empty, to when full. This means that questions take up a different amount of space when empty. You will see this means the pages will change as you fill them in. Unfortunately there is nothing I can do about that.Indefinite integralsxn dx= xn+1n+1+c, n≠1Example 1: Simple polynomialx3 dx= x3+13+1+c= x44+cExample 2: More complex polynomialx3+2x2+5 dx= x3 dx+2x2 dx+5dx= x44+2x33+ 5x+cExample 3: Much more complex polynomial – simplify first5x-32x dxExpand the numerator 5x-32=25x2-30x+9 25x2-30x+9x dx= 25x2x12 dx-30xx12 dx+ 9x12 dxApply laws of dividing indices 25x2x12= 25x2÷x12=25x2- 12=25x3230xx12= 30x1÷x12=30x1- 12=30x129x12=9x-12?25x2x12 dx-30xx12 dx+ 9x12 dx= 25x32 dx-30x12 dx+ 9x-12 dx25x32 dx=25x32+132+1= 25x525230x12 dx=30x12+112+1= 30x32329x-12 dx=9x-12+1-12+1= 9x1212?25x2x12 dx-30xx12 dx+ 9x12 dx= 25x5252-30x3232+9x1212+c= 10x52-20x32+18x+c410988414133800Mathswatch the following Q1 x4 dxx4 dx= x4+14+1+cx FORMTEXT ????? FORMTEXT ?????+cQ2x5 dxx5 dx= x FORMTEXT ?????+1 FORMTEXT ?????+1+cx FORMTEXT ????? FORMTEXT ?????+cQ3x6 dxx6 dx= x FORMTEXT ????? FORMTEXT ?????+cQ42x6 dx2x6 dx= 2x FORMTEXT ????? FORMTEXT ?????+cQ53x6 dx3x6 dx= 3x FORMTEXT ????? FORMTEXT ?????+cQ63x12 dx3x12 dx= FORMTEXT ?????x FORMTEXT ????? FORMTEXT ????? FORMTEXT ????? FORMTEXT ?????+c= FORMTEXT ?????x FORMTEXT ????? FORMTEXT ?????+ FORMTEXT ?????Q73x-12 dx3x-12= FORMTEXT ?????x FORMTEXT ????? FORMTEXT ????? FORMTEXT ????? FORMTEXT ?????+c= FORMTEXT ?????x FORMTEXT ????? FORMTEXT ?????+ FORMTEXT ?????Q83x-2 dx3x-2= 3x FORMTEXT ????? FORMTEXT ?????+ FORMTEXT ?????= FORMTEXT ?????x FORMTEXT ?????+ FORMTEXT ?????Q9 3x6+4x2 dx=3x6 dc +4x2 dx=3x FORMTEXT ????? FORMTEXT ?????+4 x FORMTEXT ????? FORMTEXT ?????+ FORMTEXT ?????Q10 3x6+4x2+2x dx=3x6 dc +4x2 +2xdx=3x FORMTEXT ????? FORMTEXT ?????+4 x FORMTEXT ????? FORMTEXT ?????+2 x FORMTEXT ????? FORMTEXT ?????+ FORMTEXT ?????=3x FORMTEXT ????? FORMTEXT ?????+4 x FORMTEXT ????? FORMTEXT ?????+ x FORMTEXT ?????+ FORMTEXT ?????Q11 3x6+4x2+2x+4 dx=3x6 dc +4x2 +2x+ 4dx= FORMTEXT ?????x FORMTEXT ????? FORMTEXT ?????+ FORMTEXT ????? x FORMTEXT ????? FORMTEXT ?????+x FORMTEXT ?????+ FORMTEXT ?????x+ FORMTEXT ?????Q12 3x6+4x2+2x12+4 dx=3x6 dc +4x2 +2x12+ 4dx= FORMTEXT ?????x FORMTEXT ????? FORMTEXT ?????+ FORMTEXT ????? x FORMTEXT ????? FORMTEXT ?????+ FORMTEXT ????? x FORMTEXT ????? FORMTEXT ????? FORMTEXT ????? FORMTEXT ?????+ FORMTEXT ?????x + FORMTEXT ?????= FORMTEXT ?????x FORMTEXT ????? FORMTEXT ?????+ FORMTEXT ????? x FORMTEXT ????? FORMTEXT ?????+ FORMTEXT ????? x FORMTEXT ????? FORMTEXT ????? FORMTEXT ?????+ FORMTEXT ?????x + FORMTEXT ?????Q13 6x-3x3 dx=6xx3 dx- 3x3 dx=6x2 dx- 3x3 dx= FORMTEXT ????? x FORMTEXT ?????+ FORMTEXT ????? FORMTEXT ?????x FORMTEXT ?????+ FORMTEXT ?????= FORMTEXT ?????- FORMTEXT ?????x2x FORMTEXT ?????+ FORMTEXT ?????Q146x-3x4 dx=6xx4 dx- 3x4 dx= FORMTEXT ?????x FORMTEXT ????? dx- FORMTEXT ?????x FORMTEXT ????? dx= FORMTEXT ????? x FORMTEXT ?????+ FORMTEXT x FORMTEXT ?????+ FORMTEXT ?????= FORMTEXT ?????- FORMTEXT ?????xx FORMTEXT ?????+ FORMTEXT ?????Q156x-32x4 dx6x-32= FORMTEXT ?????x2- FORMTEXT ?????x+ FORMTEXT ?????= FORMTEXT ?????x2- FORMTEXT ?????x+ FORMTEXT ?????x4 dx= FORMTEXT ?????x FORMTEXT ????? dx- FORMTEXT ?????x FORMTEXT ????? dx+ FORMTEXT ?????x FORMTEXT ????? dx= FORMTEXT ?????x+ FORMTEXT ?????x FORMTEXT ?????- FORMTEXT ?????x FORMTEXT ?????+ FORMTEXT ????? Independent practiceNow complete Ex 13B (minimum: 10 – 15)Definite integralsYou can calculate an integral between two limits. This is called the definite integral. A definite integral produces a value. An indefinite integral produces a function.Example 1: Simple polynomialExample 2: More complex polynomial1218x-4x3 dx= 1218x dx- 124x3 dx9x2+2x212=36+12-9+236.5-11=25.5424745312954000MathsWatch the following definite integralsQ1 01x2 dx=x3301=13-0= FORMTEXT ?????3Q2 04x2 dx=x3304= FORMTEXT ?????3-0= FORMTEXT ?????3Q3 24x2 dx=x3324= FORMTEXT ?????3- FORMTEXT ?????3= FORMTEXT ?????3Q4 24x3 dx=x FORMTEXT ????? FORMTEXT ?????24= FORMTEXT ?????- FORMTEXT ?????= FORMTEXT ?????Q5 24x-3 dx=x FORMTEXT ????? FORMTEXT ?????24= FORMTEXT ????? FORMTEXT ?????- FORMTEXT ????? FORMTEXT ?????= FORMTEXT ????? FORMTEXT ?????Q6 24x-32 dx=x FORMTEXT ????? FORMTEXT ????? FORMTEXT ????? FORMTEXT ?????24= FORMTEXT ?????- FORMTEXT ?????= FORMTEXT ?????Q8 02x2+3x dx=x33+ 3x2202=83+122-0= FORMTEXT ?????3Q904x2+3x dx=x33+ 3x2204= FORMTEXT ?????3+ FORMTEXT ?????2-0= FORMTEXT ?????3Q1024x2+3x dx=x33+ 3x2224= FORMTEXT ?????3+ FORMTEXT ?????2- FORMTEXT ?????3+ FORMTEXT ?????2= FORMTEXT ?????3Q1124x3+3x dx=x FORMTEXT ????? FORMTEXT ?????+ 3x2224= FORMTEXT ????? FORMTEXT ?????+ FORMTEXT ?????2- FORMTEXT ????? FORMTEXT ?????+ FORMTEXT ?????2= FORMTEXT ?????Q1124x3+3x2 dx=x FORMTEXT ????? FORMTEXT ?????+ x FORMTEXT ?????24= FORMTEXT ????? FORMTEXT ?????+ FORMTEXT ?????- FORMTEXT ????? FORMTEXT ?????+ FORMTEXT ?????= FORMTEXT ?????Q1124x3+3x2x dx=24x3x dx+ 243x2x dx=24x FORMTEXT ????? FORMTEXT ????? dx+ 243x FORMTEXT ????? FORMTEXT ????? dx= FORMTEXT ?????x FORMTEXT ????? FORMTEXT ????? FORMTEXT ?????+ FORMTEXT ?????x FORMTEXT ????? FORMTEXT ????? FORMTEXT ?????24= FORMTEXT ????? FORMTEXT ?????+ FORMTEXT ????? FORMTEXT ?????-2 FORMTEXT ?????77+6 FORMTEXT ?????55= FORMTEXT ????? 2dpIndependent practiceNow complete Ex 13D (minimum: 5 – 8) ................
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