The rate of change in the volume of a tank is known to be dV/dt=0.6t*cos(0.08t^2 -1), where V(t) is in gallons per minute and 0<=t<=10 (0 is less than or equal to t which is less than or equal to 10). If the tank has a volume of 14 gallons initially, what is its volume at 10 minutes?

Answer 1

dv/dt = 0.6t cos(0.08t^2-1)
v = 3/8 sin(0.08t^2-1) + c
Since v(0) = 14, c = 14+3/8 sin(1) = 14.3

v(t) = .375 sin(.08t^2-1)+14.3
Now just evaluate v(10)