A research probe measures the rate of accumulation of cosmic dust, DDD, on a satellite's surface over time, ttt, in years. The rate is modelled by the function:
dDdt=58t4−27t5+3 \frac{dD}{dt} = \frac{5}{8}t^4 - \frac{2}{7t^5} + \sqrt{3} dtdD=85t4−7t52+3Find the general expression for D(t)D(t)D(t) by evaluating:
∫(58t4−27t5+3)dt \int \left( \frac{5}{8}t^4 - \frac{2}{7t^5} + \sqrt{3} \right) dt ∫(85t4−7t52+3)dtsimplifying your answer.
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.
