The rate of depletion of a mineral resource, R(t)R(t)R(t) in gigatonnes per decade, is modeled by the formula
R(t)=7t62−53t6+14,t≥1R(t) = \frac{7t^6}{2} - \frac{5}{3t^6} + \frac{1}{4}, \quad t \ge 1R(t)=27t6−3t65+41,t≥1
where t t\,t is the number of decades since the start of industrial mining.
Determine the general expression for the total quantity of the resource depleted, ∫R(t) dt\int R(t) \, dt∫R(t)dt, giving each term in its 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.