Integrals Of Trigonometric Functions Trivia Quiz

20 Questions | Total Attempts: 1020

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Integrals Of Trigonometric Functions Trivia Quiz

How well do you remember the integrals of the trigonometric functions? For this quiz, you must know how to do integrations using various trigonometric identities, solving some questions for us. This quiz is best to strengthen your basics and prepare for an upcoming exam. All the Best! .


Questions and Answers
  • 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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