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1.11.5 Integration by substitution and by parts (A-level only)

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Question 6

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.

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1.11.5 Integration by substitution and by parts (A-level only) Questions

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  3. /1.11.5 Integration by substitution and by parts (A-level only)