calc 2

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Hint

∫0dx =

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Hint

C

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Hint

∫[g(x) + h(x)]dx =

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Hint

G(x) + H(x) + C

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Calculus

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45 Terms

1
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∫0dx =

C

2
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∫[g(x) + h(x)]dx =

G(x) + H(x) + C

3
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∫xⁿdx =

1/n+1 * x^(n+1) + C

4
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∫e^xdx =

e^x + C

5
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∫sin(x)dx =

-cos(x) + C

6
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∫sec²(x)dx =

tan(x) + C

7
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∫sec(x)tan(x)dx =

sec(x) + C

8
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∫⅟√(1-x²)dx =

arcsin(x) + C

9
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∫kdx =

kx + C

10
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∫kf(x)dx =

kF(x) + C

11
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∫1/x dx =

ln(abs(x)) + C

12
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∫a^x dx =

a^x / lna + C

13
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∫cos(x)dx =

sin(x) + C

14
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∫csc²(x)dx =

-cot(x) + C

15
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∫csc(x)cot(x)dx =

-csc(x) + C

16
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∫⅟(1+x²) dx =

arctan(x) + C

17
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∫tan(x)dx =

ln(abs(sec(x))) + C

18
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∫cot(x)dx =

ln(abs(sin(x))) + C

19
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∫sec(x)dx =

ln(abs(secx + tanx)) + C

20
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∫csc(x)dx =

ln(abs(cscx - cotx)) + C

21
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∫ln(x)dx =

xlnx - x + C

22
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substitution for √a²-x²

x = a*sin(theta)

23
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substitution for √a²+x²

x = a*tan(theta)

24
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substitution for √x²-a²

x = a*sec(theta)

25
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1-sin²x =

cos^2 (x)

26
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1 + tan²x =

sec^2 (x)

27
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sec²x - 1 =

tan^2 (x)

28
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√a²+x² becomes

a*sec(theta)

29
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√x²-a² becomes

a*tan(theta)

30
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√a²-x² becomes

a*cos(theta)

31
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Integration by parts

integral(udv) = u*v - integral(v*du)

32
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LIATE

Logarithm, Inverse trig, Algebraic, Trigonometric, Exponential

33
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sin(2x) =

2sin(x)cos(x)

34
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sin²x (power reduction) =

(1 - cos(2x))/2

35
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cos²x (power reduction) =

(1 + cos(2x))/2

36
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sinAcosB =

1/2(sin(A+B) + sin(A-B))

37
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sinAsinB =

1/2(cos(A-B) - cos(A+B))

38
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cosAcosB = `

1/2(cos(A-B) + cos(A+B))

39
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∫⅟(a²+x²) dx =

1/a * arctan(x/a) + C

40
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average value of f on [a, b]

1/(b-a) * integral from a to b of [f(x)dx]

41
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Arc length L of f(x) on [a, b]

L = ∫[sqrt(1 + (dy/dx)^2) dx] on [a,b]

42
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Surface area in terms of x across the x-axis

SA = ∫[2πf(x) * sqrt(1 + (dy/dx)^2) dx] on [a,b]

43
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Surface area in terms of x across the y-axis

SA = integral from a to b of [2 pi x * sqrt(1 + (dy/dx)^2) dx]

44
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Surface area in terms of y across the x-axis

SA = integral from a to b of [2 pi y * sqrt(1 + (dx/dy)^2) dy]

45
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Surface area in terms of y across the y-axis

SA = integral from a to b of [2 pi g(y) * sqrt(1 + (dx/dy)^2) dy]