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1 9 x 8 4 x 2 dx 1 2 1 2 u 2

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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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