1. Find the average value of the function {image} on the interval [1, 4].1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

2. Find the average value of the function {image} on the interval {image} .1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

3. In a certain city the temperature x hours after 2 A. M
In a certain city the temperature x hours after 2 A.M. was modeled by the function {image} Find the average temperature during the period from 2 A.M. to 2 P.M.
14.201
38.274
39.437
41.934 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

4. The velocity v of blood that flows in a blood vessel with radius R and length l at a distance r from the central axis is {image} where P is the pressure difference between the ends of the vessel and q is the viscosity of the blood. Suppose that Vessel 1 has length 1.6 cm and outer radius 0.5 mm, and Vessel 2 has length 4.1 cm and outer radius 0.8 mm. Find the average velocities (with respect to r) over the interval {image} for each vessel. Which vessel has the higher average velocity?
Vessel 2
Vessel 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

5. Household electricity in a certain former Soviet republic is supplied in the form of alternating current that varies from 104 V to -104 V with a frequency of 60 cycles per second (Hz). The voltage is thus given by the equation {image} where t is the time in seconds. Voltmeters read the RMS (root-mean-square) voltage, which is the square root of the average value of {image} over one cycle. Calculate the RMS voltage of household current.
5,408
104 52
73.54 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50