A researcher determines that the rate of expansion of a specialized polymer, V V\,V mm3^33, with respect to time t t\,t seconds, is modeled by the equation:
dVdt=30t5+16t3−14t8,t>0 \frac{dV}{dt} = 30t^5 + 16t^3 - \frac{14}{t^8}, \quad t > 0 dtdV=30t5+16t3−t814,t>0Find a general expression for V V\,V in terms of ttt, giving your answer in its simplest form.
Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
