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Date May 2019 Marks available 7 Reference code 19M.2.AHL.TZ1.H_7
Level Additional Higher Level Paper Paper 2 Time zone Time zone 1
Command term Find Question number H_7 Adapted from N/A

Question

The function f is defined by f(x)=(x1)2x ≥ 1 and the function g is defined by g(x)=x2+1x ≥ 0.

The region R is bounded by the curves y=f(x)y=g(x) and the lines y=0x=0 and y=9 as shown on the following diagram.

The shape of a clay vase can be modelled by rotating the region R through 360˚ about the y-axis.

Find the volume of clay used to make the vase.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

volume =π90(y12+1)2dyπ91(y1)dy      (M1)(M1)(M1)(A1)(A1)

Note: Award (M1) for use of formula for rotating about y-axis, (M1) for finding at least one inverse, (M1) for subtracting volumes, (A1)(A1)for each correct expression, including limits.

=268.6100.5(85.5π32π)

=168(=53.5π)       A2

[7 marks]

Examiners report

[N/A]

Syllabus sections

Topic 5—Calculus » AHL 5.12—Areas under a curve onto x or y axis. Volumes of revolution about x and y
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Topic 5—Calculus

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