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