Use the substitution u=1+tu = 1 + \sqrt{t}u=1+t to show that the integral
∫12t1+t dt\int \frac{12\sqrt{t}}{1+\sqrt{t}} \, dt∫1+t12tdt
can be written in the form
∫(24u−48+24u) du\int \left( 24u - 48 + \frac{24}{u} \right) \, du∫(24u−48+u24)du
The mass of a fungal colony, mmm grams, grows at a rate modelled by the equation
dmdt=12t1+t\frac{dm}{dt} = \frac{12\sqrt{t}}{1+\sqrt{t}}dtdm=1+t12t
where ttt is the number of days since the colony was first observed, for 1≤t≤91 \le t \le 91≤t≤9.
Determine the total increase in the mass of the colony from the end of day 1 to the end of day 9. Show each stage of your working and give your answer to one decimal place.
Practise Edexcel A Level Maths 11.5 Integration by Substitution with exam-style questions for A Level Maths. 59 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.