Determine ∫(10t4−6t3) dt\int \left( 10t^4 - \frac{6}{\sqrt[3]{t}} \right) \, dt ∫(10t4−3t6)dt.
The rate of change of the mass, MMM grams, of a synthetic crystal with respect to time, ttt hours, is modeled by the differential equation
dMdt=10t4−6t3,t>0 \frac{dM}{dt} = 10t^4 - \frac{6}{\sqrt[3]{t}}, \quad t > 0 dtdM=10t4−3t6,t>0After 8 hours of growth, the mass of the crystal is measured to be 65520 grams.
Find an expression for MMM in terms of ttt.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions 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, 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.
