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+3
Find 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)dt
simplifying your answer.
Practise Edexcel A Level Maths 11.1 Integrating Standard Functions with exam-style questions for A Level Maths. 81 questions, 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.