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)=(x−1)2, x ≥ 1 and the function g is defined by g(x)=x2+1, x ≥ 0.
The region R is bounded by the curves y=f(x), y=g(x) and the lines y=0, x=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 =π∫90(y12+1)2dy−π∫91(y−1)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.
=268.6…−100.5…(85.5π−32π)
=168(=53.5π) A2
[7 marks]