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.
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.