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 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.
