Integration (3) Flashcards

1
Q

What is ∫ cotx dx?

A

ln|sinx| + C

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2
Q

ln|sinx| + C

A

What is ∫ cotx dx?

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3
Q

What is ∫ cosecx dx?

A

-ln|cosecx + cotx| + C

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4
Q

-ln|cosecx + cotx| + C

A

What is ∫ cosecx dx?

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5
Q

What is ∫ secx dx?

A

ln|secx + tanx| + C

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6
Q

ln|secx + tanx| + C

A

What is ∫ secx dx?

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7
Q

What is sec^2 pheta?

A

1 + tan^2 pheta

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8
Q

1 + tan^2 pheta

A

What is sec^2 pheta?

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9
Q

What is cosec^2 pheta?

A

1 + cot^2 pheta

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10
Q

1 + cot^2 pheta

A

What is cosec^2 pheta?

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11
Q

What is ∫ (6x^5)(e^x^6) dx?

A

e^x^6 + C

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12
Q

e^x^6 + C

A

What is ∫ (6x^5)(e^x^6) dx?

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13
Q

What is ∫ e^sinx cosx dx?

A

e^sinx + C

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14
Q

e^sinx + C

A

What is ∫ e^sinx cosx dx?

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15
Q

What do differential equations have?

A

A dy/dx term

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16
Q

A dy/dx term

A

What do differential equations have?

17
Q

What is the starting condition?

A

t=0

18
Q

t=0

A

What is the starting condition?

19
Q

What is integration by parts?

A

u*v - ∫(v * (du/dx) dx)

20
Q

u*v - ∫(v * (du/dx) dx)

A

What is integration by parts?

21
Q

Process for integration by substitition

A

Find u, integrate u to get du/dx

Rearrange du/dx to make dx the subject

Substitute dx at the end of the original equation

Integrate it