The cross-section of a custom-designed architectural support beam is modelled by the region RRR. This region is bounded by the xxx-axis and the curve CCC with equation y=(x2−8x)lnx,x>0y = (x^2 - 8x) \ln x, \quad x > 0y=(x2−8x)lnx,x>0 as shown in the design specifications. The region RRR lies entirely below the xxx-axis and represents the profile of the beam's underside between its two support anchors on the horizontal axis.
Show that the area of the cross-section RRR can be written in the form p+qln2p + q \ln 2p+qln2 where ppp and qqq are rational constants to be determined.
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.