Course home

11.6 Integration by Parts

Question 4

The cross-section of a custom-designed architectural support beam is modelled by the region $R$ . This region is bounded by the $x$ -axis and the curve $C$ with equation

(x^2 - 8x) \ln x, \quad x > 0

as shown in the design specifications. The region $R$ lies entirely below the $x$ -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 $R$ can be written in the form

\ln 2

where $p$ and $q$ are rational constants to be determined.

[9]

Markscheme

11.6 Integration by Parts Questions

A Level
Maths
11.6 Integration by Parts

52 exam-style questions on Edexcel A Level Maths 11.6 Integration by Parts. Each one has a worked solution and a mark scheme showing where the marks go.

11.6 Integration by Parts

Question bank

11.6 Integration by Parts

Easy Medium Hard

1 2 3 4 5 6 7 8

Question 4

The cross-section of a custom-designed architectural support beam is modelled by the region $R$ . This region is bounded by the $x$ -axis and the curve $C$ with equation

(x^2 - 8x) \ln x, \quad x > 0

as shown in the design specifications. The region $R$ lies entirely below the $x$ -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 $R$ can be written in the form

\ln 2

where $p$ and $q$ are rational constants to be determined.

[9]

Markscheme

11.6 Integration by Parts Questions

A Level
Maths
11.6 Integration by Parts

52 exam-style questions on Edexcel A Level Maths 11.6 Integration by Parts. Each one has a worked solution and a mark scheme showing where the marks go.