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Question 104

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

Integration Questions

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

864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.

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