calculus 2 trig identities & integrals

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19 Terms

1
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substitute cos(2x) with

cosĀ²x-sinĀ²x

2
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substitute sinxcosx with

Ā½sin(2x)

3
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substitute sin(2x) with

2sinxcosx

4
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substitute sinĀ²x with (name both)

Ā½(1-cos(2x))

1-cosĀ²x

5
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substitute cosĀ²x with (name both)

Ā½(1+cos(2x))

1-sinĀ²x

6
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Strategy for integrating even powers of sin and cos

Use half angle identities

sinĀ²x = Ā½(1 āˆ’ cos(2x))

cosĀ²x = Ā½(1 + cos(2x))

sin(2x) = 2sinxcosx

7
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Strategy for even powers of sec

1.) Factor out a secĀ²x.

2.) Replace the remaining even powers of secant using secĀ²x = 1 + tanĀ²x

3.) Let u = tanx and integrate.

8
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Strategy for odd powers of sin

1.) Factor out one power of sine.

2.) Replace the remaining even powers of sine using sinĀ²x = 1 āˆ’ cosĀ²x

3.) Let u = cosx and integrate.

9
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Strategy for odd powers of cos

1.) Factor out one power of cosine.

2.) Replace the remaining even powers of sine using cosĀ²x = 1 āˆ’ sinĀ²x

3.) Let u = sinx and integrate.

10
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Strategy for odd powers of tan

1.) Factor out a secxtanx.

2.) Replace the remaining powers of tangent using tanĀ²x = secĀ²x āˆ’ 1

3.) Let u = secx and integrate.

11
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āˆ«b^x

b^x/lnb

12
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āˆ«secx dx

ln|secx+tanx|+C

13
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āˆ«cscx dx

ln|cscx-cotx|+C

14
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āˆ«tanx dx

ln|secx|+C

15
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āˆ«cotx dx

ln|sinx|+C

16
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āˆ«cscĀ²x dx

-cotx + C

17
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graph of sinx

knowt flashcard image
18
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graph of cosx

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19
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graph of tanx

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