Skip to content

Course home

1.8 Integration

1.8 Integration

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119
Question 83

A landscape architect is designing a decorative concrete partition for a park. The height of the partition, HHH metres, at a horizontal distance ddd metres from a central pillar, is modeled by the equation

H=24d+9,d≥−2.25 H = 2\sqrt{4d + 9}, \quad d \ge -2.25 H=24d+9​,d≥−2.25

A straight support beam, represented by line lll, is attached to the partition at the point P(4,10)P(4, 10)P(4,10). The beam is perpendicular to the curve of the partition at PPP.

a.

Use calculus to show that an equation for the line lll is

5d+4H−60=0 5d + 4H - 60 = 0 5d+4H−60=0
[4]
b.

The region RRR is the cross-sectional area of the partition's side, bounded by the curve, the ground (the line H=0H = 0H=0), and the support beam lll.

Use algebraic integration to find the exact area of RRR.

[6]
Markscheme

1.8 Integration Questions

  1. A Level
  2. /Maths
  3. /1.8 Integration

160 exam-style questions on WJEC A Level Maths 1.8 Integration, covering 1.8.1 Integration, 1.8.2 Integration, and 1.8.3 Integration. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank