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Evalute the integral ∫ (7x^2+8x+8)/(x) dx from (e,1)?

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  • Evalute the integral ∫ (7x^2+8x+8)/(x) dx from (e,1)?


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Answer #1 | 08/02 2014 12:39
Simplify, then integrate (7x + 8 + 8/x) * dx Integrate (7/2) * x^2 + 8x + 8 * ln|x| + C From e to 1 (7/2) * (1^2 - e^2) + 8 * (1 - e) + 8 * (ln|1| - ln|e|) => (7/2) * (1 - e^2) + 8 * (1 - e) + 8 * (0 - 1) =< (7/2) * (1 - e^2) + 8 * (1 - e) - 8 => (1/2) * (7 * (1 - e^2) + 16 * (1 - e) - 16) => (1/2) * (7 - 7e^2 + 16 - 16e - 16) => (1/2) * (7 - 16e - 7e^2)
Answer #2 | 09/02 2014 07:30
∫ (7x^2+8x+8)/(x) dx = 7 ∫ x dx + 8 ∫ dx + ∫ 8 / x dx = (7/2) x^2 + 8x + 8 ln(x) Let F(x) = (7/2) x^2 + 8x + 8 ln(x) F(1) = 7/2+8+8ln(1) = 23/2 F(e) = 7e^2/2 + 8e+8 = 55.608 F(1) - F(e) = 11.50 - 55.608 = -44.108

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