test 4_1 - R ' t = 30 10 t where t is measured in months....

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Test #4 Integrals Chapters 6-7 Take-home test Part I: evaluating integrals Evaluate the integrals. Show all work. Give answers either as exact answers, or rounded to the nearest hundredth. 1. x 2 1 x dx 2. e 3 t dt 3. 1 6 x x 3 dx 4. 0 2 x 1 x 2 2 x 5 dx 5. 6 1 x x 3 dx 6. 1 1 x x 3 dx
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Part II 7. Estimate the area under the curve y =− x 2 4 x 5 from x = 2 to x = 5 using R 3 and L 3 . Since y is decreasing over this interval, is R 3 going to be an over-estimate or an under-estimate for the area? Explain your answer. Use these estimates to give an upper and lower bound for the area: _______ Area _________ How many rectangles would be needed to guarantee that this calculation is within .1 of the actual value? 1 0 8 6 4 2 -2 5 1 0 y = -x^2 + 4x + 5
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8. What is the average value of the function f x = x x 3 from x = 1 to x = 6? 9. A taxi company finds that the rate, in dollars, of repairs for its cars can be modeled by the function
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Unformatted text preview: R ' t = 30 10 t where t is measured in months. How much more is the company spending on maintenance of one-year-old cars ( t = 12) than six-month-old cars? Assuming that R (0) = 0, what is the total amount spent on maintenance over the first year? (Since R (0) = 0, the change in maintenance costs from t = 0 to t = 12 is the total amount of the cost.) Part III 10. Find the area bounded by the curves y = x 2 and y = x 6 . 11. Find the area between the curves y = ln x and y = 1 x from x = 1 e to x = e . A. Set up the integral needed to solve this. B. Use a calculator to evaluate this to the nearest hundredth. I pledge that I have neither given nor received help on this test. _______________________________________________ ________________ (signature) (date)...
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test 4_1 - R ' t = 30 10 t where t is measured in months....

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