Exam 1 Formulas Flashcards

1
Q

integration by parts

A

∫u dv = uv - ∫v du

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2
Q

d/dx arcsin

A

1/√(1-x²)

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3
Q

d/dx arccos

A

-(1/√(1-x²))

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4
Q

d/dx arctan

A

1/(1+x²)

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5
Q

√(a²-x²)

A

x=asinθ

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6
Q

√(a²+x²)

A

x=atanθ

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7
Q

√(x²-a²)

A

x=asecθ

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8
Q

trapezoidal rule

A

Δx/2( f(x0) + 2f(x1) + … + 2f(x(n-1)) + f(xn)

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9
Q

p-series convergent integrals

A

∫1/(x^p)dx (p>1)

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10
Q

p-series divergent integrals

A

∫(1/x^p) (p=<1)

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11
Q

∫tanx dx

A

ln|secx| + C

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12
Q

∫cotx dx

A

ln|sinx| + C

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13
Q

∫secx dx

A

ln|secx + tanx| + C

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14
Q

∫cscx dx

A

ln|cscx - cotx| + C

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15
Q

∫sin²x dx

A

x/2 - sin2x/4 + C

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16
Q

∫cos²x dx

A

x/2 + sin2x/4 + C

17
Q

volume by slicing formula

A

∫A(x) dx (evaluated from a to b)

18
Q

disc/washer method

A

V = ∫πr² dx (evaluated from a to b)

19
Q

∫csc(x)cot(x) dx

A

-csc(x) + C

20
Q

∫sec(x)tan(x) dx

A

sec(x) + C

21
Q

∫csc²(x) dx

A

-cot(x) + C

22
Q

∫sec²(x) dx

A

tan(x) + C