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Unformatted text preview: tion. It is also called integration. We can also refer to ∫ f ( x ) dx as an indefinite integral where f ( x ) is called the integrand and x is the variable of integration. Example: Evaluate the indefinite integral. 1. ∫ 9 x 8 − 4 x + 2 dx ( ) ⎛ 1/ 2 1 2 u ⎞
2. ∫ ⎜ u + − e ⎟ du ⎝
⎠
u 3. ∫ t −2
dt 3
t Rules of Integration: Rule 1:
The Integral of a Constant k . Rule 2: ∫ k dx = kx + C , where C is any constant The Power Rule
1 n +1
∫ x dx = n + 1 x + C , ( n ≠ −1)
n Rule 3: The Integral of a Constant Multiple of a Function ∫ k ⋅ f ( x ) dx = k ∫ f ( x ) dx , where k is a constant Rule 4: The Sum/Difference Rule ⎣
⎦
∫ ⎡ f ( x ) ± g ( x )⎤ dx = ∫ f ( x ) dx ± ∫ g ( x ) dx
Rule 5: Integral of the Exponential Functio...
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This note was uploaded on 05/01/2013 for the course MATH 1081 taught by Professor Johanson during the Spring '08 term at Colorado.
 Spring '08
 JOHANSON
 Antiderivatives, Derivative

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