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.
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.
