A companyr is producing a new product. Due to the nature of the product. the time required to produce each unit ' decreases as workers become more familiar with the production procedure. It is determined that the function for the 1 learning process is Tm = 3 + 12].? [E] . where Thur} is the time. in hours. required to produce the xth unit. Find the total time required for a new worker to produce units 1 through "ID; units 4D through 5D. View an example | All parts showing to produ st X d that th the xth A company is producing a new product. Due to the nature of the product, the time required to produce each unit decreases as workers become more familiar with the production procedure. It is determined that the function for the learning process is T(x) = 5+ 0.9|x . where T(x) is the time, in hours, required to produce the xth unit. Find the total time required for a new worker to produce units 1 through 8; units 16 through 24. If T(x) is the time required to produce the xth unit, then the antiderivative of T(x) is the total time required to produce x units. To find the time required to produce units 1 to 8, use the fundamental theorem of integral calculus. First, set up the integral for the time to produce units 1 to 8. 1(5+0.9 (#)) Ox Integrate. Evaluate the result at each end point and subtract. [5x + 0.9 In x]; = 36.87 Therefore, the new worker requires about 36.87 hours to produce units 1 to 8. The process is the same to find the time required to produce units 16 through 24. The only changes are the limits of integration. Find the limits of integration to calculate the time to produce units 16 through 24 using the same method to correct for continuity. 24 1 5+0.9 () ] dx Then evaluate the integral. 24 1 5+0.9 - Ox = 15x + 0.9 Inx) 16 ~40.36 Therefore, the new worker requires about 40.36 hours to produce units 16 through 24