basic integrals

Question

During 21 weeks at the height of an influenza​ outbreak, the rate at which the number of cases of infection changed could be approximated by

I′(t)=−6.34t+142.3​,

where I is the total number of infected people and t is time measured in weeks.

​a) Estimate​ I(t), the total number of people who have contracted influenza by time t. Assume that

​I(0)=1428.

l(t)=

Answer 1

dI/dt = f(t) or dI = f(t)dt Integrate both sides (definite integral)

I - I₀ = integral from 0 to t of f(s) ds

I = 1428 - 6.34*t²/2 + 142.3t

Please consider a tutor. Take care.

Answer 2