Suppose the daily revenue of selling tacos is R(t)=100+10t where t represents the number of days from the beginning of the week and t must be greater than or equal to 0 while being less than of equal to 8. If I know my daily costs to be C(t)=90+5t (with the same limits for t) for dollars per year, how do I find the area between the graphs?

Question

Suppose the daily revenue of selling tacos is R(t)=100+10t where t represents the number of days from the beginning of the week and t must be greater than or equal to 0 while being less than of equal to 8.  If I know my daily costs to be C(t)=90+5t (with the same limits for t) for dollars per year, how do I find the area between the graphs?

oobleck · Answer

since R(t) > C(t) for t>0 the area is just ∫[0,8] R(t) - C(t) dt = ∫(100+10t)-(90+5t) dt = ∫19+5t dt