Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Question
Chapter 5, Problem 1PE
To determine
To define: The antiderivative.
Expert Solution & Answer
Answer to Problem 1PE
The reverse of derivative is called antiderivative.
Explanation of Solution
Given:The antiderivative.
The reverese order of derivative is called antideriavtive.
The symbol of antiderivative is
For example:
Antiderivative of
Where,
Now derivative of
Drivative of constant is 0
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Chapter 5 Solutions
Calculus
Ch. 5.1 - Prob. 1PSCh. 5.1 - Prob. 2PSCh. 5.1 - Prob. 3PSCh. 5.1 - Prob. 4PSCh. 5.1 - Prob. 5PSCh. 5.1 - Prob. 6PSCh. 5.1 - Prob. 7PSCh. 5.1 - Prob. 8PSCh. 5.1 - Prob. 9PSCh. 5.1 - Prob. 10PS
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Prob. 1PSCh. 5.2 - Prob. 2PSCh. 5.2 - Prob. 3PSCh. 5.2 - Prob. 4PSCh. 5.2 - Prob. 5PSCh. 5.2 - Prob. 6PSCh. 5.2 - Prob. 7PSCh. 5.2 - Prob. 8PSCh. 5.2 - Prob. 9PSCh. 5.2 - Prob. 10PSCh. 5.2 - Prob. 11PSCh. 5.2 - Prob. 12PSCh. 5.2 - Prob. 13PSCh. 5.2 - Prob. 14PSCh. 5.2 - Prob. 15PSCh. 5.2 - Prob. 16PSCh. 5.2 - Prob. 17PSCh. 5.2 - Prob. 18PSCh. 5.2 - Prob. 19PSCh. 5.2 - Prob. 20PSCh. 5.2 - Prob. 21PSCh. 5.2 - Prob. 22PSCh. 5.2 - Prob. 23PSCh. 5.2 - Prob. 24PSCh. 5.2 - Prob. 25PSCh. 5.2 - Prob. 26PSCh. 5.2 - Prob. 27PSCh. 5.2 - Prob. 28PSCh. 5.2 - Prob. 29PSCh. 5.2 - Prob. 30PSCh. 5.2 - Prob. 31PSCh. 5.2 - Prob. 32PSCh. 5.2 - Prob. 33PSCh. 5.2 - Prob. 34PSCh. 5.2 - Prob. 35PSCh. 5.2 - Prob. 36PSCh. 5.2 - Prob. 37PSCh. 5.2 - Prob. 38PSCh. 5.2 - Prob. 39PSCh. 5.2 - Prob. 40PSCh. 5.2 - Prob. 41PSCh. 5.2 - Prob. 42PSCh. 5.2 - Prob. 43PSCh. 5.2 - Prob. 44PSCh. 5.2 - Prob. 45PSCh. 5.2 - Prob. 46PSCh. 5.2 - Prob. 47PSCh. 5.2 - Prob. 48PSCh. 5.2 - Prob. 49PSCh. 5.2 - Prob. 50PSCh. 5.2 - Prob. 51PSCh. 5.2 - 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Prob. 16PSCh. 5.6 - Prob. 17PSCh. 5.6 - Prob. 18PSCh. 5.6 - Prob. 19PSCh. 5.6 - Prob. 20PSCh. 5.6 - Prob. 21PSCh. 5.6 - Prob. 22PSCh. 5.6 - Prob. 23PSCh. 5.6 - Prob. 24PSCh. 5.6 - Prob. 25PSCh. 5.6 - Prob. 26PSCh. 5.6 - Prob. 27PSCh. 5.6 - Prob. 28PSCh. 5.6 - Prob. 29PSCh. 5.6 - Prob. 30PSCh. 5.6 - Prob. 31PSCh. 5.6 - Prob. 32PSCh. 5.6 - Prob. 33PSCh. 5.6 - Prob. 34PSCh. 5.6 - Prob. 35PSCh. 5.6 - Prob. 36PSCh. 5.6 - Prob. 37PSCh. 5.6 - Prob. 38PSCh. 5.6 - Prob. 39PSCh. 5.6 - Prob. 40PSCh. 5.6 - Prob. 41PSCh. 5.6 - Prob. 42PSCh. 5.6 - Prob. 43PSCh. 5.6 - Prob. 44PSCh. 5.6 - Prob. 45PSCh. 5.6 - Prob. 46PSCh. 5.6 - Prob. 47PSCh. 5.6 - Prob. 48PSCh. 5.6 - Prob. 49PSCh. 5.6 - Prob. 50PSCh. 5.6 - Prob. 51PSCh. 5.6 - Prob. 52PSCh. 5.6 - Prob. 53PSCh. 5.6 - Prob. 54PSCh. 5.6 - Prob. 55PSCh. 5.6 - Prob. 56PSCh. 5.6 - Prob. 57PSCh. 5.6 - Prob. 58PSCh. 5.6 - Prob. 59PSCh. 5.6 - Prob. 60PSCh. 5.7 - Prob. 1PSCh. 5.7 - Prob. 2PSCh. 5.7 - Prob. 3PSCh. 5.7 - Prob. 4PSCh. 5.7 - Prob. 5PSCh. 5.7 - Prob. 6PSCh. 5.7 - Prob. 7PSCh. 5.7 - Prob. 8PSCh. 5.7 - Prob. 9PSCh. 5.7 - Prob. 10PSCh. 5.7 - Prob. 11PSCh. 5.7 - Prob. 12PSCh. 5.7 - Prob. 13PSCh. 5.7 - Prob. 14PSCh. 5.7 - Prob. 15PSCh. 5.7 - Prob. 16PSCh. 5.7 - Prob. 17PSCh. 5.7 - Prob. 18PSCh. 5.7 - Prob. 19PSCh. 5.7 - Prob. 20PSCh. 5.7 - Prob. 21PSCh. 5.7 - Prob. 22PSCh. 5.7 - Prob. 23PSCh. 5.7 - Prob. 24PSCh. 5.7 - Prob. 25PSCh. 5.7 - Prob. 26PSCh. 5.7 - Prob. 27PSCh. 5.7 - Prob. 28PSCh. 5.7 - Prob. 29PSCh. 5.7 - Prob. 30PSCh. 5.7 - Prob. 31PSCh. 5.7 - Prob. 32PSCh. 5.7 - Prob. 33PSCh. 5.7 - Prob. 34PSCh. 5.7 - Prob. 35PSCh. 5.7 - Prob. 36PSCh. 5.7 - Prob. 37PSCh. 5.7 - Prob. 38PSCh. 5.7 - Prob. 39PSCh. 5.7 - Prob. 40PSCh. 5.7 - Prob. 41PSCh. 5.7 - Prob. 42PSCh. 5.7 - Prob. 43PSCh. 5.7 - Prob. 44PSCh. 5.7 - Prob. 45PSCh. 5.7 - Prob. 46PSCh. 5.7 - Prob. 47PSCh. 5.7 - Prob. 48PSCh. 5.7 - Prob. 49PSCh. 5.7 - Prob. 50PSCh. 5.7 - Prob. 51PSCh. 5.7 - Prob. 52PSCh. 5.7 - Prob. 53PSCh. 5.7 - Prob. 54PSCh. 5.7 - Prob. 55PSCh. 5.7 - Prob. 56PSCh. 5.7 - Prob. 57PSCh. 5.7 - Prob. 58PSCh. 5.7 - Prob. 59PSCh. 5.7 - Prob. 60PSCh. 5.8 - Prob. 1PSCh. 5.8 - Prob. 2PSCh. 5.8 - Prob. 3PSCh. 5.8 - Prob. 4PSCh. 5.8 - Prob. 5PSCh. 5.8 - Prob. 6PSCh. 5.8 - Prob. 7PSCh. 5.8 - Prob. 8PSCh. 5.8 - Prob. 9PSCh. 5.8 - Prob. 10PSCh. 5.8 - Prob. 11PSCh. 5.8 - Prob. 12PSCh. 5.8 - Prob. 13PSCh. 5.8 - Prob. 14PSCh. 5.8 - Prob. 15PSCh. 5.8 - Prob. 16PSCh. 5.8 - Prob. 17PSCh. 5.8 - Prob. 18PSCh. 5.8 - Prob. 19PSCh. 5.8 - Prob. 20PSCh. 5.8 - Prob. 21PSCh. 5.8 - Prob. 22PSCh. 5.8 - Prob. 23PSCh. 5.8 - Prob. 24PSCh. 5.8 - Prob. 25PSCh. 5.8 - Prob. 26PSCh. 5.8 - Prob. 27PSCh. 5.8 - Prob. 28PSCh. 5.8 - Prob. 29PSCh. 5.8 - Prob. 30PSCh. 5.8 - Prob. 31PSCh. 5.8 - Prob. 32PSCh. 5.8 - Prob. 33PSCh. 5.8 - Prob. 34PSCh. 5.8 - Prob. 35PSCh. 5.8 - Prob. 36PSCh. 5.8 - Prob. 37PSCh. 5.8 - Prob. 38PSCh. 5.8 - Prob. 39PSCh. 5.8 - Prob. 40PSCh. 5.8 - Prob. 41PSCh. 5.8 - Prob. 42PSCh. 5.8 - Prob. 43PSCh. 5.8 - Prob. 44PSCh. 5.8 - Prob. 45PSCh. 5.8 - Prob. 46PSCh. 5.8 - Prob. 47PSCh. 5.8 - Prob. 48PSCh. 5.8 - Prob. 49PSCh. 5.8 - Prob. 50PSCh. 5.8 - Prob. 51PSCh. 5.8 - Prob. 52PSCh. 5.8 - Prob. 53PSCh. 5.8 - Prob. 54PSCh. 5.8 - Prob. 55PSCh. 5.8 - Prob. 56PSCh. 5.8 - Prob. 57PSCh. 5.8 - Prob. 58PSCh. 5.8 - Prob. 59PSCh. 5.8 - Prob. 60PSCh. 5.9 - Prob. 1PSCh. 5.9 - Prob. 2PSCh. 5.9 - Prob. 3PSCh. 5.9 - Prob. 4PSCh. 5.9 - Prob. 5PSCh. 5.9 - Prob. 6PSCh. 5.9 - Prob. 7PSCh. 5.9 - Prob. 8PSCh. 5.9 - Prob. 9PSCh. 5.9 - Prob. 10PSCh. 5.9 - Prob. 11PSCh. 5.9 - Prob. 12PSCh. 5.9 - Prob. 13PSCh. 5.9 - Prob. 14PSCh. 5.9 - Prob. 15PSCh. 5.9 - Prob. 16PSCh. 5.9 - Prob. 17PSCh. 5.9 - Prob. 18PSCh. 5.9 - Prob. 19PSCh. 5.9 - Prob. 20PSCh. 5.9 - Prob. 21PSCh. 5.9 - Prob. 22PSCh. 5.9 - Prob. 23PSCh. 5.9 - Prob. 24PSCh. 5.9 - Prob. 25PSCh. 5.9 - Prob. 26PSCh. 5.9 - Prob. 27PSCh. 5.9 - Prob. 28PSCh. 5.9 - Prob. 29PSCh. 5.9 - Prob. 30PSCh. 5.9 - Prob. 31PSCh. 5.9 - Prob. 32PSCh. 5.9 - Prob. 33PSCh. 5.9 - Prob. 34PSCh. 5.9 - Prob. 35PSCh. 5.9 - Prob. 36PSCh. 5.9 - Prob. 37PSCh. 5.9 - Prob. 38PSCh. 5.9 - Prob. 39PSCh. 5.9 - Prob. 40PSCh. 5.9 - Prob. 41PSCh. 5.9 - Prob. 42PSCh. 5.9 - Prob. 43PSCh. 5.9 - Prob. 44PSCh. 5.9 - Prob. 45PSCh. 5.9 - Prob. 46PSCh. 5.9 - Prob. 47PSCh. 5.9 - Prob. 48PSCh. 5.9 - Prob. 49PSCh. 5.9 - Prob. 50PSCh. 5.9 - Prob. 51PSCh. 5.9 - Prob. 52PSCh. 5.9 - Prob. 53PSCh. 5.9 - Prob. 54PSCh. 5.9 - Prob. 55PSCh. 5.9 - Prob. 56PSCh. 5.9 - Prob. 57PSCh. 5.9 - Prob. 58PSCh. 5.9 - Prob. 59PSCh. 5.9 - Prob. 60PSCh. 5 - Prob. 1PECh. 5 - Prob. 2PECh. 5 - Prob. 3PECh. 5 - Prob. 4PECh. 5 - Prob. 5PECh. 5 - Prob. 6PECh. 5 - Prob. 7PECh. 5 - Prob. 8PECh. 5 - Prob. 9PECh. 5 - Prob. 10PECh. 5 - Prob. 11PECh. 5 - Prob. 12PECh. 5 - Prob. 13PECh. 5 - Prob. 14PECh. 5 - Prob. 15PECh. 5 - Prob. 16PECh. 5 - Prob. 17PECh. 5 - Prob. 18PECh. 5 - Prob. 19PECh. 5 - Prob. 20PECh. 5 - Prob. 21PECh. 5 - Prob. 22PECh. 5 - Prob. 23PECh. 5 - Prob. 24PECh. 5 - Prob. 25PECh. 5 - Prob. 26PECh. 5 - Prob. 27PECh. 5 - Prob. 28PECh. 5 - Prob. 29PECh. 5 - Prob. 30PECh. 5 - Prob. 1SPCh. 5 - Prob. 2SPCh. 5 - Prob. 3SPCh. 5 - 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Prob. 60SPCh. 5 - Prob. 61SPCh. 5 - Prob. 62SPCh. 5 - Prob. 63SPCh. 5 - Prob. 64SPCh. 5 - Prob. 65SPCh. 5 - Prob. 66SPCh. 5 - Prob. 67SPCh. 5 - Prob. 68SPCh. 5 - Prob. 69SPCh. 5 - Prob. 70SPCh. 5 - Prob. 71SPCh. 5 - Prob. 72SPCh. 5 - Prob. 73SPCh. 5 - Prob. 74SPCh. 5 - Prob. 75SPCh. 5 - Prob. 76SPCh. 5 - Prob. 77SPCh. 5 - Prob. 78SPCh. 5 - Prob. 79SPCh. 5 - Prob. 80SPCh. 5 - Prob. 81SPCh. 5 - Prob. 82SPCh. 5 - Prob. 83SPCh. 5 - Prob. 84SPCh. 5 - Prob. 85SPCh. 5 - Prob. 86SPCh. 5 - Prob. 87SPCh. 5 - Prob. 88SPCh. 5 - Prob. 89SPCh. 5 - Prob. 90SPCh. 5 - Prob. 91SPCh. 5 - Prob. 92SPCh. 5 - Prob. 93SPCh. 5 - Prob. 94SPCh. 5 - Prob. 95SPCh. 5 - Prob. 96SPCh. 5 - Prob. 97SPCh. 5 - Prob. 98SPCh. 5 - Prob. 99SPCh. 5 - Prob. 1CRPCh. 5 - Prob. 2CRPCh. 5 - Prob. 3CRPCh. 5 - Prob. 4CRPCh. 5 - Prob. 5CRPCh. 5 - Prob. 6CRPCh. 5 - Prob. 7CRPCh. 5 - Prob. 8CRPCh. 5 - Prob. 9CRPCh. 5 - Prob. 10CRPCh. 5 - Prob. 11CRPCh. 5 - Prob. 12CRPCh. 5 - Prob. 13CRPCh. 5 - Prob. 14CRPCh. 5 - Prob. 15CRPCh. 5 - Prob. 16CRPCh. 5 - Prob. 17CRPCh. 5 - Prob. 18CRPCh. 5 - Prob. 19CRPCh. 5 - Prob. 20CRPCh. 5 - Prob. 21CRPCh. 5 - Prob. 22CRPCh. 5 - Prob. 23CRPCh. 5 - Prob. 24CRPCh. 5 - Prob. 25CRPCh. 5 - Prob. 26CRPCh. 5 - Prob. 27CRPCh. 5 - Prob. 28CRPCh. 5 - Prob. 29CRPCh. 5 - Prob. 30CRPCh. 5 - Prob. 31CRPCh. 5 - Prob. 32CRPCh. 5 - Prob. 33CRPCh. 5 - Prob. 34CRPCh. 5 - Prob. 35CRPCh. 5 - Prob. 36CRPCh. 5 - Prob. 37CRPCh. 5 - Prob. 38CRPCh. 5 - Prob. 39CRPCh. 5 - Prob. 40CRPCh. 5 - Prob. 41CRPCh. 5 - Prob. 42CRPCh. 5 - Prob. 43CRPCh. 5 - Prob. 44CRPCh. 5 - Prob. 45CRPCh. 5 - Prob. 46CRPCh. 5 - Prob. 47CRPCh. 5 - Prob. 48CRPCh. 5 - Prob. 49CRPCh. 5 - Prob. 50CRPCh. 5 - Prob. 51CRPCh. 5 - Prob. 52CRPCh. 5 - Prob. 53CRPCh. 5 - Prob. 54CRPCh. 5 - Prob. 55CRPCh. 5 - Prob. 56CRPCh. 5 - Prob. 57CRPCh. 5 - Prob. 58CRPCh. 5 - Prob. 59CRPCh. 5 - Prob. 60CRP
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- cotinine levels measured in a group of nonsmokers exposed to tobacco smoke (n = 40, Mean = 60.58 ng>mL, s = 138.08 ng>mL) and a group of nonsmokers not exposed to tobacco smoke (n = 40, Mean = 16.35 ng>mL, s = 62.53 ng>mL). Cotinine is a metabolite of nicotine, meaning that when nicotine is absorbed by the body, cotinine is produced. Use a 0.05 significance level to test the claim that nonsmokers exposed to tobacco smoke have a higher mean cotinine level than nonsmokers not exposed to tobacco smoke. State null & alternative hypothesis What kind of test would this be - two tailed, left tailed or right tailed? The t test would be appropriate for testing this claim. Why is that?arrow_forwardWhat does l’Hospital’s Rule say?arrow_forwardAntiderivative of: 0.9t2 + 0.04t + 5arrow_forward
- Process 1 Process 2 Process 3 60 45 50 58 40 52 55 35 56 62 34 47 68 52 48 52 49 52 64 48 51 66 39 50 One-way ANOVA: Process 1, Process 2, Process 3 Source DF ss MS F P Treatment 2 1282.8 Error 21 578.9 Total 23 1861.7 A health food company wants to determine the best process for blanching dark green vegetable material so it can be added to other food products without losing vitamin A. They are examining three different blanching processes to determine which is best in terms of vitamin A retention (mg/100mg). The data collected and partial ANOVA results appears above. The F-statistic value is F = 27.57. O F = 2.215. O F = 23.267. F = 3.22.arrow_forwardOverproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma.f Over a period of months, an adult male patient has taken seven blood tests for uric acid. The concentration was x = 5.35 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with o = 1.77 mg/dl. (a) Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error? (Round your answers to two decimal places.) lower limit upper limit margin of error (b) What conditions are necessary for your calculations? (Select all that apply.) O o is unknown O normal distribution of uric acid O n is large Oo is known O uniform distribution of uric acid (c) Interpret your results in the context of this problem. O The probability that this interval contains the true average uric acid level for this patient is 0.05. O The probability that…arrow_forwardTrue or False?arrow_forward
- I need typingarrow_forwarddoes the result indicate whether the treatment is effective?arrow_forwardhelp thank you! Suppose a researcher is interested in the effectiveness in a new childhood exercise program implemented in a SRS of schools across a particular county. In order to test the hypothesis that the new program decreases BMI (Kg/m2), the researcher takes a SRS of children from schools where the program is employed and a SRS from schools that do not employ the program and compares the results. Assume the following table represents the SRSs of students and their BMIs. Student Intervention Group: Group 1BMI(kg/m2)Student Control Group: Group 2BMI(kg/m2)A18.6A21.6B18.2B18.9C19.5C19.4D18.9D22.6E24.1F23.6Assuming that all the necessary conditions are met (normality, independence, etc.) carry out the appropriate statistical test to determine if the new exercise program could decrease BMI (Kg/m2). Use an alpha level of 0.05 X=BMI mu_1 (?1): mean BMI of population from which Group 1 was sampled mu_2 (?2): mean BMI of population from which Group 2 was sampled What is the P-valule?…arrow_forward
- The recommended intake for Calcium for adults is 1000 mg per day. A researcher is interested to determine if adults with high income level have more calcium intake than the recommended amount. A hypothesis test is conducted. What is the alternative hypothesis?arrow_forwardSince the days of the Pharaohs, people in Egypt suffered the ravages of a parasite called schisosomaisis that is found in the mud of Nile delta. To reduce the spread of infection, between 1918 to 1982, some western countries helped perform inoculation in the general Egyptian population. However, with little care taken to disinfect the syringes and needles, a large portion of the Egyptian population became infected with a deadly form of hepatitis virus -- the hepatitis C virus, (HCV) which was not recognized at that time. The result of that debacle is that Egypt now has the highest prevalence of hepatitis C in the world. In order to quantify the extent of its spread, a simple random sample of n = 3888 people showed 973 individuals exposed to the hepatitis C virus. (i) Find a 95\% confidence interval for p, the true proportion of the Egyptian population infected with the Hepatitis C virus. (ii) Had we wanted to find a 95\% confidence interval for p, with width w being 1 percentage point,…arrow_forwardThere has been concern for some time that nitrite present in cured meats may result in the formation of carcinogenic N-nitrosamines in the stomach by reaction with amines in the diet. It is possible to safely measure the amount of nitrosamine production in humans by administering a large dose of proline and measuring the level of N-nitroso-proline, a non-toxic reaction product, excreted in the urine. You decide to test the hypothesis that eating a reasonable amount of cured meat will increase the amount of nitrosation taking place in the stomach in the following way. Each of 6 subjects, who have been asked to avoid cured meats for the previous week, is given a dose of proline and the excretion of N-nitroso-proline is measured for 24 hours. Each subject is then fed a breakfast including 6 strips of bacon and a dose of proline; excretion of the nitrosated amino acid is again measured for 24 hours. You obtain the data listed below in the form (basal µg excreted, µg excreted after bacon).…arrow_forward
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