IB Math SL - Santowski1 T4.2 – Multiplication of Matrices IB Math SL - Santowski.
Ib maths sl antiderivatives
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Anti-derivatives. Indefinite Integrals By the end of this lesson you will be able to: • Understand the integration process as the reverse process of differentiation. • Calculate the integrals of powers of x and any linear combination of them.
Transcript of Ib maths sl antiderivatives
- 1. Anti-derivatives. Indefinite Integrals Bytheendofthislessonyouwillbeableto: Understandtheintegrationprocessasthe reverseprocessofdifferentiation. Calculatetheintegralsofpowersofxandany linearcombinationofthem.
2. fisafunctionwhosederivativeisf'(x)=2xthenf(x)=orf(x)= orf(x)=ingeneralf(x)= fistheantiderivativeoff' 3. Thesetofalltheantiderivativesofafunctionis calledtheindefiniteintegralofthefunction So:Note:Sometimeswewrite:F(x)tomeantheintegraloff(x).Sowe have F(x)= f(x)dx 4. f(x)f'(x)x x2 x3 xn1)Multiplybythepower 2)Subtract1tothepowerf'(x)f(x)1xx2 nx1)Add1tothepower 2)Dividebythepower 5. Ingeneral: 6. (( 7. ThegradientfunctionofafunctionHish(x)=x+1 WhatisthefunctionH?IfthegraphofthefunctionHpassesthrough(1,4), givetheequationofH. 8. Aparticularcurvehas Wearetoldthatthecurvepassesthroughthepoint(2,5). Findtheequationofthecurve. 9. differentiation s=displacementintegration 10. Theaccelerationams2ofaparticlemovingina straightlineisgivenbya=t+1.Findformulae forthevelocityandthedisplacementifs=0and v=8whent=0. 11. AttachmentsIntegral=Sum.swf
