The rate of change of the volume of water, VVV, being pumped into a reservoir is modeled by the equation
dVdt=7t24−52t4+23 \frac{dV}{dt} = \frac{7t^2}{4} - \frac{5}{2t^4} + \frac{2}{3} dtdV=47t2−2t45+32where VVV is measured in cubic metres and ttt is the time in hours since pumping began. Determine the general expression for VVV in terms of ttt, giving each term 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.
