Assignment 16-solutions

# Assignment 16-solutions - nanni(arn437 Assignment 16...

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nanni (arn437) – Assignment 16 – guntel – (54940) 1 This print-out should have 4 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points ±ind the total area under the graph oF y = 6 x 3 For x 1 . 1. Area = 4 2. Area = 5 2 3. Area = 7 2 4. Area = 5. Area = 2 6. Area = 3 correct Explanation: The total area under the graph For x 1 is an improper integral whose value is the limit lim t →∞ i t 1 6 x 3 dx . Now i t 1 6 x - 3 dx = - 3 b x - 2 B t 1 . Consequently, Area = lim t 3 b 1 - t - 2 B = 3 . 002 10.0 points Determine iF the improper integral I = i 3 0 2 ln x x dx converges, and iF it does, compute its value. 1. I = (ln 3) 2 2. I does not converge correct 3. I = 2(ln 3) 2 4. I = 2 ln 3 5. I = ln 3 Explanation: The integral is improper because lim x 0 + ln x x = -∞ , so we have to consider lim t 0 + I t , I t = i 3 t 2 ln x x dx . To evaluate I t , set u = ln x. Then du = dx x , while x = t = u = ln t , x = 3 = u = ln 3 .

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Assignment 16-solutions - nanni(arn437 Assignment 16...

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