The rate of vertical ascent, dhdt\frac{dh}{dt}dtdh in metres per minute, of a weather balloon is modelled by the expression:
dhdt=(3t−2)(4t+3)(3t+2)\frac{dh}{dt} = (3t - 2)(4t + 3)(3t + 2)dtdh=(3t−2)(4t+3)(3t+2)
where ttt is the time in minutes. Find the general expression for the height hhh of the balloon at time ttt, writing your answer in simplest form.
Practise Edexcel A Level Maths 11.1 Integrating Standard Functions with exam-style questions for A Level Maths. 81 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.