CAB-Chp-5ishB-NTsampASN2 - CalcAB Chp 5ishB Trigonometric...

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CalcAB Chp 5ishB Trigonometric Anti-derivatives NOTES 1. REM: ANTI-DERIVATIVE / INTEGRAL undoes a derivative Notation for anti-derivative: = F(x) + C the symbol that looks like a lazy letter S is the symbol to work the anti-derivative “ f(x) dx “ is the differential derivative Flow chart of the different aspects of anti-derivatives: 2. SOME ANTI-DERIVATIVE/INTEGRAL TRIG FORMULAS (a) = sinx + C (b) = cosx + C (c) = secx + C (d) = cscx + C (e) = tanx + C (f) = cotx + C Ex Integrate each. (During time in class I recommend you make notes to yourself about any of the trig identities you may not remember later on.) (a) dx (b) dx (c) dx (d) dx <answers> (a) F(x) = 6tanx + C (b) F(x) = secx+ C (c) F(x) = tanx + C (d) F(x) = 2x 2 5cscx + C Anti-derivative Integral INDEFINITE integral F(x) + C or F(x) + # GENERAL solution F(x) + C PARTICULAR solution F(x) + # DEFINITE integral (number answer, not an equation)
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3. PARTICULAR SOLUTIONS Ex Find the particular solution f(x) of each using the given information. (a) f
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This note was uploaded on 02/21/2011 for the course MATH 408C taught by Professor Knopf during the Spring '10 term at University of Texas at Austin.

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CAB-Chp-5ishB-NTsampASN2 - CalcAB Chp 5ishB Trigonometric...

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