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Question 58

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)ln⁡x,x>0 y = (x^2 - 8x) \ln x, \quad x > 0 y=(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+qln⁡2 p + q \ln 2 p+qln2

where ppp and qqq are rational constants to be determined.

[9]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

864 exam-style questions on Edexcel A Level Maths Integration, 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. Each one has a worked solution and a mark scheme showing where the marks go.

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