Trigonometric Integral Identities For Calculus

20 Questions  I  By Kirakiwibug
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 Trigonometric Integral Identities For Calculus
This is a basic quiz to help memorization of various trigonometric identities in calculus, many of which must be memorized for use on exams.

  
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  • 1. 
    ∫sin(u)du
    • A. 

      Ln|secu + tanu)| + C

    • B. 

      Tan(u)+C

    • C. 

      Sec(u)+C

    • D. 

      -cos(u) + C

    • E. 

      Cos(u)+C


  • 2. 
    ∫cos(u)du
    • A. 

      Sin(u)+C

    • B. 

      Ln|sin(u)| + C

    • C. 

      -cot(u) + C

    • D. 

      (1/a)arcsec(|u|/a) + C

    • E. 

      -csc(u) + C


  • 3. 
    ∫tan(u)du
    • A. 

      -ln|cos(u)| + C

    • B. 

      (1/a)arctan(u/a) + C

    • C. 

      -sec^2(u) + C

    • D. 

      Csc(u)*cot(u)

    • E. 

      -cot(u) + C


  • 4. 
    ∫cot(u)du
    • A. 

      Ln|sin(u)| + C

    • B. 

      (1/a)arctan(u/a) + C

    • C. 

      -cot(u) + C

    • D. 

      Sin(u)+C

    • E. 

      Ln|secu + tanu)| + C


  • 5. 

    ∫du/(a^2 - u^2)
    • A. 

      Arctan(u/a) + C

    • B. 

      Arcsin(u/a) + C

    • C. 

      (1/a) arcsin (u/a) + C

    • D. 

      (1/u) arcsin (|u|/a) + C

    • E. 

      (1/a) arcsec (|u|/a) + C


  • 6. 

    ∫du/(a^2 + u^2)
    • A. 

      (1/u) arcsin (|u|/a) + C

    • B. 

      Arctan(u/a) + C

    • C. 

      Arcsin(u/a) + C

    • D. 

      (1/a) arctan (u/a) + C

    • E. 

      (1/a) arctan (|u|/a) + C


  • 7. 

    ∫du/((u(u^2 - a^2))^.5)
    • A. 

      (1/a) arctan (u/a) + C

    • B. 

      Arcsin(u/a) + C

    • C. 

      (1/a)arcsec(u/a) + C

    • D. 

      (1/a) arctan (|u|/a) + C

    • E. 

      (1/a)arcsec(|u|/a) + C


  • 8. 
    ∫csc(u)cot(u)du
    • A. 

      Csc(u) + C

    • B. 

      -csc^2(u) + C

    • C. 

      Sec(u)tan(u) + C

    • D. 

      Tan(u) + C

    • E. 

      -csc(u) + C


  • 9. 
    ∫csc(u)du
    • A. 

      Ln|csc(u) + cot(u)| + C

    • B. 

      Tan^2(u) + C

    • C. 

      -ln|csc(u) + cot(u)| + C


  • 10. 
    Cos^2(x) = 
    • A. 

      (1 + cos(2x)) / 2

    • B. 

      (1 - cos (2x)) / 2


  • 11. 
    Sin^2(x) =
    • A. 

      (1 - cos (2x)) / 2

    • B. 

      (1 + cos(2x)) / 2


  • 12. 
    If the power of the cosine is odd and positive...
    • A. 

      Save a sine factor

    • B. 

      Save a cosine factor

    • C. 

      Convert the remaining factors into sines

    • D. 

      Convert the remaining factors into cosines


  • 13. 
    If the power of the cosine is odd and positive,
    • A. 

      Save a sine factor

    • B. 

      Save a cosine factor

    • C. 

      Convert the remaining factors into sines

    • D. 

      Convert the remaining factors into cosines


  • 14. 
    If the powers of both the sine and cosine are even and positive,
    • A. 

      Save a sine factor

    • B. 

      Save a cosine factor

    • C. 

      Use the sine^2 and cosine^2 identities

    • D. 

      Convert the remaining factors into sines

    • E. 

      Convert the remaining factors into cosines


  • 15. 
    If the power of the secant is even and positive,
    • A. 

      Save a secant squared factor

    • B. 

      Convert the remaining factors into tangents

    • C. 

      Save a secant-tangent factor

    • D. 

      Convert the remaining factors into secants

    • E. 

      Expand and integrate


  • 16. 
    If the power of the tangent is odd and positive,
    • A. 

      Save a secant squared factor

    • B. 

      Save a secant-tangent factor

    • C. 

      Convert the remaining factors into tangents

    • D. 

      Convert the remaining factors into secants

    • E. 

      Expand and integrate


  • 17. 
    If there are no secant factors and the power of the tangent is even and positive,
    • A. 

      Convert a tangent-squared factor into a secant-squared factor

    • B. 

      Save a secant-tangent factor

    • C. 

      Save a secant squared factor


  • 18. 
    For integrals involving √(a^2 - u^2),
    • A. 

      U = asinΘ

    • B. 

      U = tanΘ

    • C. 

      U=secΘ

    • D. 

      √(a^2 - u^2) = acosΘ

    • E. 

      √(u^2 - a^2) = atanΘ


  • 19. 
    For integrals involving √(a^2 + u^2)
    • A. 

      U = asinΘ

    • B. 

      U = atanΘ

    • C. 

      U=asecΘ

    • D. 

      √(a^2 + u^2) = acosΘ

    • E. 

      √(u^2 + a^2) = asecΘ


  • 20. 
    For integrals involving √(u^2 - a^2)
    • A. 

      U = asinΘ

    • B. 

      U = atanΘ

    • C. 

      U=asecΘ

    • D. 

      √(u^2 - a^2) = acosΘ

    • E. 

      √(u^2 - a^2) = atanΘ


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