Find ∫2x2e−4x dx\int 2x^2 e^{-4x} \, dx∫2x2e−4xdx writing 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 > 1dtdV=(t−1)(2t+1)10t+2,t>1 where 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 11.7 Partial Fractions with exam-style questions for A Level Maths. 19 questions, 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.