A marine biologist models the rate of change of the depth of a diving seal, DDD (in metres), relative to time sss (in seconds) for s>0 s > 0\,s>0 using the following formula:
dDds=7s34−35s23+27 \frac{dD}{ds} = \frac{7s^3}{4} - \frac{3}{5\sqrt[3]{s^2}} + \frac{2}{7} dsdD=47s3−53s23+72Determine the general equation for the depth D D\,D in terms of sss, giving your answer in its simplest form.
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.