Exam 2 Flashcards

1
Q

∫x^n dx

A

1/n+1 X^n+1 +C

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2
Q

∫1/x dx

A

ln|x|+C

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3
Q

∫1/(ax+b)dx

A

1/a ln|a+b|+C

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4
Q

∫lnax dx

A

x(lnax -1)

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5
Q

∫a^x dx

A

a^x /lna +C

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5
Q

∫e^x dx

A

e^x +c

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6
Q

∫cscxdx

A

ln|tanx/2|+C

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7
Q

∫csc^2(ax)dx

A

-1/a cot(ax)+C

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8
Q

∫sin(ax) dx

A

-1/a cos(ax)+C

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8
Q

∫secx *cscx dx

A

ln|tanx|+C

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9
Q

∫cos(ax)

A

1/asin(ax)+C

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10
Q

∫tan(ax) dx

A

-1/a ln(cos(ax)) +C

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11
Q

∫sec^2 (ax) dx

A

1/a tan(ax) +C

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12
Q

∫sec(x)tan(x) dx

A

secx +C

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13
Q

∫secx dx

A

ln|secx+tanx|+C

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14
Q

work

A

(a to b)∫ F(x) dx

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15
Q

Force of spring

A

spring constant * distance stretched

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16
Q

Force of y

A

mass *gravity

17
Q

what is density * volume

18
Q

∫lnx dx

A

x(lnx-1)+C

19
Q

∫du / sqrt(a^2 - u^2)

A

sin^-1 (u/a)+C

19
Q

∫log(base a)x

A

x/lna (lnx-1)+C

20
Q

∫du/ a^2 +u^2

A

1/a tan^-1 (u/a)+C

21
Q

work for water

A

(a to b) ∫densitygravityarea*x

22
∫du/ u(sqrt(u^2 -a^2)
1/a sec^-1(u/a) +C
23
∫udv
uv -∫ vdu +C
24
LIATE
Log , inverse trig, alegriaic, trig, exponential
25
integrating sin+cos products with odd power trig
1. write odd as even power * 1 of it 2.get it in terms of the other 3. integrate making u the higher power
26
integrating sin+cos products with both even powers
1. double angle identities to get into polynomial of cos(2x) 2. apply strategies to things with powers greater than 1
27
double angle cos^2(x)
1/2 (1+cos(2x)
28
double angle for sin^2(x)
1/2 (1-cos(2x))
29
identity for cos^2(x)
1-sin^2(x)
29
identity for sin^2(x)
1-cos^2(x)
30
sin(ax)cos(bx)
1/2 sin((a+b)x +1/2 sin ((a-b)x)
31
cos(ax)cos(bx)
1/2 cos((a+b)x +1/2 cos ((a-b)x)
32
tan is even sec is odd
1. write tan in terms of secx 2. write polynomial in sec 3 reduction method
32
integrating tan+sec products with sec being even
1.split out a sec^2(x) while keeping secx to even power 2.u sub with tan as u
33
integrating sin+cos products with odd power tan
1. split out secxtanx 2 write tan in even power 3. u is secx
34
identity of sec^2(x)
tan^2(x) +1
35
tan reduction formula tan^n (x) dx
1/n-1 tan^(n-1) (x) - ∫tan^ (n-2) (x)dx
36
sec reduction formula sec^n (x) dx
1/n-1 sec^(n-2) (x)tan(x) + n-2/(n-1) ∫tan^ (n-2) (x)dx
37
trig sub a^2-x^2
x = asin(theta)
38
trig sub a^2 + x^2
x = atan(theta)
39
trig sub x^2 - a^2
x = a(sec(theta)