Determine the indefinite integral ∫e−tsin(2t) dt\int e^{-t} \sin(2t) \, dt∫e−tsin(2t)dt.
A surge of electrical power, P P\,P kilowatts, in an experimental circuit is modeled by the function P(t)=e−tsin(2t),t≥0P(t) = e^{-t} \sin(2t), \quad t \ge 0P(t)=e−tsin(2t),t≥0 where t t\,t is the time in seconds since the circuit was activated.
Show that the total energy EEE (in kilojoules) transferred during the first pulse of power, which occurs between t=0t = 0t=0 and the first time t>0 t > 0\,t>0 where P(t)=0P(t) = 0P(t)=0, is exactly 25(1+e−π/2)\displaystyle \frac{2}{5}(1 + e^{-\pi/2})52(1+e−π/2).
Practise Edexcel A Level Maths 11.6 Integration by Parts with exam-style questions for A Level Maths. 52 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.