A marine biologist models the rate of change of nutrient density DDD with respect to the depth hhh (in meters) of a water column as:
dDdh=7h5−414h6,h>0 \frac{dD}{dh} = \frac{7h^5 - 4}{14h^6}, \quad h > 0 dhdD=14h67h5−4,h>0Find an expression for DDD in terms of hhh, 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.