Calc II chap 8

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Author:
lacythecoolest
ID:
284968
Filename:
Calc II chap 8
Updated:
2014-10-05 23:48:23
Tags:
IP antiderivative limitlaw partialfractiondecomposition
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Description:
integration by parts, basic antiderivative formulas, limit law, limit facts, partial fraction decomposition,
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  1. procedure for integration by parts
    • 1. choose dv-most difficult part that can use basic or substitution
    • 2. rest is u
    • 3. differentiate u to get du
    • 4. substitute into IP formula uv - |vdu
    • 5. integrate to finish
  2. what do you do if you have a definite integration with IP?
    complete IP before FTC
  3. formula for IP
    uv-|vdu
  4. AD
    |kdx=
    kx + C
  5. AD
    |k f(x)dx=
    k |f(x)
  6. AD
    |cosxdx=
    sinx + C
  7. AD
    |sinxdx
    -cosx + C
  8. AD
    |sec^2xdx=
    tanx + C
  9. AD
    |csc^2xdx=
    -cotx +C
  10. AD
    |secxtanxdx=
    secx + C
  11. AD
    |cscxcotxdx=
    -cscx + C
  12. AD
    |tanxdx=
    -ln|cosx| + C
  13. AD
    |cotxdx=
    ln|sinx| + C
  14. AD
    |secxdx=
    ln|secx + tanx| + C
  15. AD
    | cscxdx=
    -ln|cscx + cotx| + C
  16. AD
    a^xdx=
    • (1/lna)(a^x) + C
    • a cannot = 1
  17. AD
    e^xdx=
    e^x + C
  18. AD
    lnxdx=
    xlnx - x + C
  19. AD
    1/xdx=
    ln|x| + C
  20. AD
    x^-1dx
    ln|x| + C
  21. AD
    1/☑1-x^2 dx=
    arcsinx + C
  22. AD
    1/1+x^2 dx=
    arctanx + C
  23. AD
    1/x☑x^2-1 dx=
    arcsec|x| + C
  24. what 2 rules are not for integrals?
    • product
    • quotient
  25. lim[f(x) * g(x)]=
    lim f(x) * lim g(x)
  26. lim c=
    c
  27. lim x =
    a
  28. lim x^n =
    a^n
  29. limit fact
    number/0=
    +/- infinity
  30. limit fact
    number/+/-infinity=
    0
  31. limit fact
    +-infinity/number=
    +-infinity
  32. limit fact
    +-infinity/+-infinity=
    L'Hopitals rule
  33. L'Hopital's Rule
    Lim f'(x)/g'(x)
  34. limit fact composite
    f and g func. that lim g(x)=b and f is cont @b. Then.....
    lim f(g(x))=f(b)
  35. limit fact squeeze theorem
    f(x)◀g(x)◀h(x) on interval w/a
    if lim f(x)=L and lim h(x)=L, then...
    lim g(x)=L
  36. partial fract decomp
    simple linear:
    (A/x-c1) + (B/x-c2).....
  37. part fract decomp
    repeated linear
    numerator/(x-c)^n=
  38. part fract decomp
    irreducible quadratic
    (Ax+B)/(ax^2+bx+c)
  39. 5 steps for partial fraction decomposition
    • 1. only if numerator is smaller then denominator
    • 2. completely factor denominator
    • 3. set og rat func=to part fract decomp
    • 4. multiply each term by og fact denom
    • 5. choose x values to eliminate terms and solve

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