An oil rig breaks and begins to leak oil into the arctic ocean at an increasing rate of R(t) = 20t + 20 litres per day. At the instant of breakage (t=0), 100 litres of oil was spilled into the ocean via the emergency release valve. What is the equation V(t), the amount of oil (in litres) leaked into the ocean at time t days?

Question

how do i use integrals?

Answer 1

So 20t +20 L/day is the rate of spilling oil
that is, dV/dt = 20t+20
V = 10t^2 + 20t + c
given: when t = 0, V = 100, then c = 100

V(t) = 10t^2 + 20t + 100