Find
∫2x2e−4x dx \int 2x^2 e^{-4x} \, dx ∫2x2e−4xdxwriting the answer in simplest form.
The rate of change of the volume of water in a reservoir, VVV (in megalitres per hour), is modeled by the equation
dVdt=10t+2(t−1)(2t+1),t>1 \frac{dV}{dt} = \frac{10t+2}{(t-1)(2t+1)}, \quad t > 1 dtdV=(t−1)(2t+1)10t+2,t>1where t t\,t is the time in hours since a valve was opened. Use partial fractions and algebraic integration to show that the total change in volume between t=2t = 2t=2 and t=4t = 4t=4 is lnk \ln k\,lnk megalitres, where k k\,k is a fully simplified rational constant to be found.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, matched to the Edexcel A Level Maths (9MA0) 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.
