Calc II Flashcards

1
Q

integrate:

xn dx

A

xn+1
n+1

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2
Q

integrate:

k dx

A

kx + C

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3
Q

integrate:

ex dx

A

ex + C

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4
Q

integrate:

ax dx

A

ax +C
ln|a|

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5
Q

integrate:

1
x

A

ln|x|+C

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6
Q

integrate:

sin(x) dx

A

-cos(x) + C

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7
Q

integrate:

cos(x) dx

A

sin(x) + C

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8
Q

integrate:

sec2(x) dx

A

tan(x) + C

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9
Q

integrate:

csc2(x) dx

A

-cot(x) + C

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10
Q

integrate:

sec(x)tan(x) dx

A

sec(x) + C

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11
Q

integrate:

csc(x)cot(x) dx

A

-csc(x) + C

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12
Q

integrate:

______1______
√  ̄1-x2

A

sin-1(x) + C

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13
Q

integrate:

1
x2-1

A

tan-1(x) + C

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14
Q

integrate:

tan(x) dx

A

ln|sec(x)| + C

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15
Q

integrate:

sec(x) dx

A

ln|sec(x) + tan(x)| + C

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16
Q

integrate:

1
x2+a2

A

(1/a) tan-1(x/a)) +C

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17
Q

trig identities:

sin2(x)+cos2(x)

A

= 1

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18
Q

trig identities:

tan2(x) + 1

A

sec2(x)

19
Q

trig identities:

1 + cot2(x)

A

csc2(x)

20
Q

trig identities:

cos2(x)

A

(1/2)(1 + cos(2x))

21
Q

trig identities:

sin2(x)

A

(1/2)(1 - cos(2x))

22
Q

trig identities:

sin(2x)

A

2 sin(x)cos(x)

23
Q

trig identities:

cos(2x)

A

cos2(x) - sin2(x)

24
Q

substitute:

______
√ a2 - x2

A

x = a sin(θ)

25
Q

substitute:

______
√ x2 - a2

A

x = a sec(θ)

26
Q

substitute:

______
√ x2 + a2

A

x = a tan(θ)

27
Q

formula:

Area under a Polar Curve

A

∫ 1/2 πr2

28
Q

formula:

Integration By Parts (∫ udv)

A

∫udv = uv - ∫vdu

29
Q

formula:

washer method .

A

pi ∫R^2 - r^2 .

30
Q

shell method .

A

2pi ∫ rh dx .

31
Q

series tests:

if lim an =/= 0 .

A

an = divergent
nth term test

32
Q

if lim an = 0 .

A

INCONCLUSIVE .

33
Q

if ∫an = definite ..

A

series is convergent
integral test

34
Q

uh

if ∫an = indefinite ..

A

series is divergent
integral test

35
Q

sum 1
np
p <= 1

A

divergent
p-series .

36
Q

1
np
p > 1

A

convergent
p-series.

37
Q

sum of a geometric series

A

first term
( 1 - ratio)

38
Q
A
39
Q
A
40
Q
A
41
Q
A
42
Q
A
43
Q
A
44
Q
A