Find the area between the curves for the given interval. What does the area represent?

Question

If the birth rate of a population is b(t)=2200+52.3t+0.74t² people per year and the death rate is d(t)=1460+28.8t people per year, find the area between these curves for 0≤t≤10. What does this area represent?

Answer 1

2200 + 52.3t + 0.74t² = 1460 + 28.8t, no real solutions. So, A = ∫₀¹⁰(0.74t² + 23.5t + 740)dt = (0.74t³/3 + 23.5t²/2 + 740t)₀¹⁰ = 740/3 + 2350/2 + 7400 = 8821 people.

This is population grow because of new born in 10 years