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.
864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.