calculus 2 trig identities & integrals

0.0(0)
studied byStudied by 11 people
learnLearn
examPractice Test
spaced repetitionSpaced Repetition
heart puzzleMatch
flashcardsFlashcards
Card Sorting

1/18

flashcard set

Earn XP

Description and Tags

Study Analytics
Name
Mastery
Learn
Test
Matching
Spaced

No study sessions yet.

19 Terms

1
New cards

substitute cos(2x) with

cos²x-sin²x

2
New cards

substitute sinxcosx with

½sin(2x)

3
New cards

substitute sin(2x) with

2sinxcosx

4
New cards

substitute sin²x with (name both)

½(1-cos(2x))

1-cos²x

5
New cards

substitute cos²x with (name both)

½(1+cos(2x))

1-sin²x

6
New cards

Strategy for integrating even powers of sin and cos

Use half angle identities

sin²x = ½(1 − cos(2x))

cos²x = ½(1 + cos(2x))

sin(2x) = 2sinxcosx

7
New cards

Strategy for even powers of sec

1.) Factor out a sec²x.

2.) Replace the remaining even powers of secant using sec²x = 1 + tan²x

3.) Let u = tanx and integrate.

8
New cards

Strategy for odd powers of sin

1.) Factor out one power of sine.

2.) Replace the remaining even powers of sine using sin²x = 1 − cos²x

3.) Let u = cosx and integrate.

9
New cards

Strategy for odd powers of cos

1.) Factor out one power of cosine.

2.) Replace the remaining even powers of sine using cos²x = 1 − sin²x

3.) Let u = sinx and integrate.

10
New cards

Strategy for odd powers of tan

1.) Factor out a secxtanx.

2.) Replace the remaining powers of tangent using tan²x = sec²x − 1

3.) Let u = secx and integrate.

11
New cards

∫b^x

b^x/lnb

12
New cards

secx dx

ln|secx+tanx|+C

13
New cards

cscx dx

ln|cscx-cotx|+C

14
New cards

tanx dx

ln|secx|+C

15
New cards

cotx dx

ln|sinx|+C

16
New cards

csc²x dx

-cotx + C

17
New cards

graph of sinx

knowt flashcard image
18
New cards

graph of cosx

knowt flashcard image
19
New cards

graph of tanx

knowt flashcard image