Integrals Of Trigonometric Functions Trivia Quiz

20 Questions | By Kirakiwibug | Last updated: Mar 22, 2022 | Total Attempts: 1669

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Integrals Of Trigonometric Functions Trivia Quiz - 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