Let w(t) be the number of widgets produced at time t. Let the rate of production (widgets per week) for widgets at a company is given by
w'(t)= 50,000(1- (1000/(t+10)^2) .
Integrate both sides of the previous differential equation from 0 to 10 to get the total production of widgets in the first 10 weeks of production. Assume that at week 0 no widgets were produced. Hint: you will need to apply the fundamental theorem of calculus and use a simple substitution. Show all details and steps.