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.
438 exam-style questions on OCR A Level Maths 1.8 Integration, covering 1.8.1 Fundamental theorem of calculus (A-level only), 1.8.2 Integrating x^n, 1.8.3 Integrating standard functions (A-level only), 1.8.4 Evaluating definite integrals, 1.8.5 Area between a curve and the x-axis, 1.8.6 Area between two curves, 1.8.7 Integration as the limit of a sum (A-level only), 1.8.8 Integration by substitution (A-level only), 1.8.9 Integration by parts (A-level only), 1.8.10 Use of partial fractions in integration (A-level only), 1.8.11 Differential equations with separable variables (A-level only), 1.8.12 Interpreting the solution of a differential equation (A-level only), and 1.8 Integration. Each one has a worked solution and a mark scheme showing where the marks go.