In a signal processing model, the power intensity P P\,P at time t t\,t is given by P(t)=t2e−2tP(t) = t^2 e^{-2t}P(t)=t2e−2t. Determine the general integral for the energy flux, ∫t2e−2t dt\int t^2 e^{-2t} \, dt∫t2e−2tdt, providing the result in its simplest factorised form.
In a chemical reaction, the rate of change of a concentration with respect to a spatial coordinate r r\,r is modeled by the function f(r)=4r+1(r+1)(2r+1)\displaystyle f(r) = \frac{4r+1}{(r+1)(2r+1)}f(r)=(r+1)(2r+1)4r+1. Use partial fractions and algebraic integration to prove that ∫134r+1(r+1)(2r+1) dr=lnk\int_{1}^{3} \frac{4r+1}{(r+1)(2r+1)} \, dr = \ln k∫13(r+1)(2r+1)4r+1dr=lnk where k k\,k is a rational constant to be determined.
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.