Exam 1 (Calculus II)

  1. integral of f(x)±g(x) dx
    integral of f(x) dx ± integral of g(x) dx
  2. integral of f(x)^n f'(x) dx
    [f(x)]^n+1/n+1 + C
  3. integral of cos(x)
    sin(x)
  4. integral of sin(x)
    -cos(x)
  5. integral of sec^2(x)
    tan(x)
  6. integral of csc^2(x)
    -cot(x)
  7. integral of sec(x)tan(x)
    sec(x)
  8. integral of -csc(x)cot(x)
    csc(x)
  9. integral of 1/f(x) dx
    ln|f(x)|
  10. integral of b^f(x)
    1/lnb ⋅ b^f(x)
  11. integral of 1/[sqrt of a^2-f(x)^2] dx
    arcsin (f(x)/a)
  12. integral of 1/[a^2+f(x)^2]
    1/a arctan(f(x)/a)
  13. integral of 1/|f(x)|[sqrt of f(x)^2 - a^2] dx
    1/a arcsec(f(x)/a)
  14. integral of tan(f(x))
    -ln|cos(f(x))| + C
  15. integral of cot(f(x))
    ln|sin(f(x))| + C
  16. integral of sec(f(x))
    ln|sec(f(x))+tan(f(x))| + C
  17. integral of csc(f(x))
    ln|csc(f(x))-cot(f(x))| + C
  18. What to do when have 1 odd trig function and an even one
    take one out of the odd then make everything the opposite of what the taken out one was
  19. what to do with one even function
    use x many half angle formulas
  20. What to do when one trig function is a square root and one is even
    split the even one using pythagorean identities
  21. What to do with one odd trig function
    take one out and use pythagorean identities
  22. what to do with mismatched functions (not related to each other)
    turn into their sin/cos versions and solve
  23. What are the three pythagorean identities?
    • sin^2x + cos^2x = 1
    • 1 + tan^2x = sec^2x
    • 1 + cot^2x = csc^2x
  24. Half angle formula for sin
    [1-cos(2x)]/2
  25. half angle formula for cos
    [1+cos(2x)]/2
  26. range for arcsin
    [-pi/2, pi/2], where y= the sin value given
  27. range for arccos
    [0, pi], where y= cos value given
  28. range for arctan
    (-pi/2, pi/2), where the value= y/x
Author
gbiebs
ID
364751
Card Set
Exam 1 (Calculus II)
Description
Updated