practice 2 answers

practice 2 answers - PRACTICE2 Name Section 1 Determine the...

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PRACTICE2 Name Section 1. Determine the average value of the function f ( x ) = 4 1 + x 2 on 0 x 3. (no decimal answers; evaluate completely) answer: AV = 1 3 i 3 0 4 1 + x 2 dx = 4 3 arctan x v v v v v 3 0 = 4 π 3 3 2. Determine the average value of the function f ( x ) = x on 1 x 36. answer: 1 35 i 36 1 x dx = 2 105 x 3 / 2 v v v v 36 1 = 430 105 3. Determine b so that the average value of f ( x ) = 2 x + 3 on [1 , b ] is 10. answer: 10 = 1 b - 1 i 10 1 (2 x + 3) dx = p x 2 + 3 x P b 1 = b 2 + 3 b - 4 b - 1 Then 10 b - 10 = b 2 + 3 b - 4 b 2 - 7 b + 6 = 0. Solve the quadratic equation and b = 6. 4. Determine c on [1 , 4] so that f ( c ) is the average value of the function f ( x ) = 3 x 2 + 2 x + 1 on [1 , 4]. (Mean Value of the Integral) answer: Frst determine average value: Av= 1 3 i 4 1 (3 x 2 + 2 x + 1) dx = 1 3 ( x 3 + x 2 + x ) v v v v 4 1 = 27 Then 3 c 2 + 2 c + 1 = 27 3 c 2 + 2 c - 26 = 0 Solve the quadratic equation.
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5. Show the evaluation of the integral. Determine the value of the improper integral
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practice 2 answers - PRACTICE2 Name Section 1 Determine the...

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