The force F in newtons) of a hydraulic cylinder in a press is proportional to th

Question

The force F in newtons) of a hydraulic cylinder in a press is proportional to the square of sec x where x is the distance (in meters) that the cylinder is extended in its cycle. The domain of F is [0, /3], and F(0)-300. (a) Find F as a function of x. rx)- 300 sec2 x F= 29772 X N (b) Find the average force exerted by the press over the interval [O, . (Round your answer to one deci mal place.) - Master It Talk to a Tutor Submit Answer Save Progress Practice Another Version My Notes Ask Your Teacher 0/1 points | Previous Answers LarCalcET6 5.4.067. The volume V, in liters, of air in the lungs during a one-second respiratory cycle is approximated by the model V0.1729t + 0.1522t2- 0.0374t3, where t is the time in seconds. Approximate the average volume of air in the lungs during one cycle. (Round your answer to four decimal places.) 1318 Need Help? Read it Talk to a Tutor

Explanation / Answer

Average value of a function f(x) over an interval [a,b] is equal to the integral of f from a to b divided by b-a.

1) Average force = integral of 300sec square x from 0 to /3 whole divided by /3. Which is = (3/).300. tan/3 = 9003/ = 496.196 Newtons.

2) Similarly here a= 0 and b = 1. So integral Will be divided by 1 only. Hence average volume is given by (0.1729/2)+(0.1522/3)-(0.0374/4)= 0.12783 liters.

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