Integration Flashcards by Audrey Harper

Q

Definite Integrals

Area under the curve
Answer is a _

A

Number

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Q

Indefinite Integrals

Antiderivative
- Sf(x)dx = _
Answer is a _

A

F(x) + c, function

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Q

sin0

A

-cos0

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Q

csc0cot0

A

-csc0

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Q

csc0csc0

A

-cot0

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Q

U-Substitution of Trig Functions

Use if inside
Sfunction(x)dx
u=x
du/dx= _
Sfunction(u)du
Solve with _

A

Derivative of x, antiderivative

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Q

First Fundamental Theorem

f(x) is continuous on [a, b]
S(ab)f(x)dx = _

A

F(b) - F(a)

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Q

U-Substitution of Functions

Use if inside
Sf(x)dx
u=x
du/dx= _
Sf(u)du
Solve with _
Make sure S(u1u2)

A

Derivative of x, antiderivative

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Q

Piecewise Functions

S(ab) |x + y|dx
x + y = _
(x function) and -(x function)
Slit up integrals and _

A

0, add

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Q

Second Fundamental Theorem

-d/dxS(ax)f(t)dt = _

A

f(x) = derivarive x f(x)

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Q

sin^20 + cos ^20

A

1

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Q

1 + tan^20

A

sec^20

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Q

1 + cot^20

A

csc^20

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Q

sin20

A

sin0cos0

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Q

cos20

A

cos^20 - sin^20

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Q

tan20

Study These Flashcards

A

(2tan0)/(1 - tan^20)