Question

Calculus Problem!!Help!!

Alabama Instruments Company has set up a production line to manufacture a new calculator. The rate of production of these calculators after t weeks is
dx/dt=5000(1−100/(t+10)^2) calculators/week.
(Notice that the production approaches 5000 per week as time goes on, but the initial production is lower because of the workers' unfamiliarity with the new techniques.)

Find the number of calculators produced from the beginning of the third week to the end of the fourth week.

Answer 1

x(t) will give the number of calculators produced over t weeks
integrate dx/dt from 2 to 4
\[5000\int\limits_{2}^{4}1 - \frac{100}{(t+10)^{2}} dt\]

Answer 2

substitute
u = t-10
du = dt

Answer 3

Thank you so much!!

Answer 4

your welcome