Find ∫(12x2−5xx) dx\int \left( 12x^2 - \dfrac{5}{x\sqrt{x}} \right) \, dx ∫(12x2−xx5)dx
The rate of change of the mass, MMM grams, of a chemical precipitate over time ttt minutes is modelled by the differential equation
dMdt=12t2−5tt,t>0 \dfrac{dM}{dt} = 12t^2 - \dfrac{5}{t\sqrt{t}}, \quad t > 0 dtdM=12t2−tt5,t>0Given that at t=4t = 4t=4, the mass of the precipitate is 265 grams, determine 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.
