5.11 Further integrationIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 5.11 Further integration

1. Water flows into a tank at a rate of $r(t)=6\sqrt{t}$ litres per minute, where $t$ is the time in minutes since the flow started. The tank is empty when $t=0$.
   Find the time taken for the volume of water in the tank to reach $500$ litres.2 marks
2. The population of a colony of bacteria changes at a rate $\dfrac{dP}{dt}=\dfrac{12}{3t+2}$ thousand per hour, where $t$ is the time in hours and $t\ge0$. At $t=0$ the population is $5$ thousand.
   Find the time at which the population reaches $20$ thousand.2 marks
3. A particle moves in a straight line. At time $t$ seconds its velocity is $v=4t\sin(t^2)$ m s$^{-1}$, where the angle is in radians. The displacement $s$ from the starting point is $0$ when $t=0$.
   Find an expression for $s$ in terms of $t$.3 marks