# Trigonometric Integral Identities For Calculus

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

Changes are done, please start the quiz.

## Questions and Answers

 1 ∫sin(u)du
 A. -cos(u) + C
 B. Cos(u)+C
 C. Ln|secu + tanu)| + C
 D. Tan(u)+C
 E. Sec(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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